M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2019
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M9100/01: Tue 12:00–12:50 M6,01011, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Learning outcomes
Student will be able to:
- numerical solving of ordinary differential equations - initial and boundary value problem - using computers
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2018
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Tue 10:00–11:50 M4,01024
  • Timetable of Seminar Groups:
M9100/01: Mon 17. 9. to Fri 14. 12. Tue 12:00–12:50 M4,01024, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba znát základní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
autumn 2017
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Wed 14:00–15:50 M6,01011
  • Timetable of Seminar Groups:
M9100/01: Mon 18. 9. to Fri 15. 12. Wed 16:00–16:50 M6,01011, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba znát základní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2016
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Mon 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M9100/01: Mon 19. 9. to Sun 18. 12. Mon 15:00–15:50 M6,01011, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2015
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 13:00–14:50 M3,01023
  • Timetable of Seminar Groups:
M9100/01: Wed 15:00–15:50 M3,01023
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2014
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M9100/01: Fri 12:00–12:50 M2,01021
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2013
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 9:00–10:50 M2,01021
  • Timetable of Seminar Groups:
M9100/01: Thu 11:00–11:50 M2,01021
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2012
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16:00–17:50 M5,01013
  • Timetable of Seminar Groups:
M9100/01: Mon 18:00–18:50 M5,01013, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • 2.Variational methods for solving ordinary differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2011
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17:00–18:50 M1,01017
  • Timetable of Seminar Groups:
M9100/01: Mon 19:00–19:50 M1,01017, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • 2.Variational methods for solving ordinary differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2010
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 MS1,01016
  • Timetable of Seminar Groups:
M9100/01: Fri 10:00–10:50 MS1,01016, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • 2.Variational methods for solving ordinary differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 11:00–12:50 M5,01013
  • Timetable of Seminar Groups:
M9100/01: Tue 13:00–13:50 M5,01013, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations and basic principles of methods for solving partial differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • Methods for solving partial differential equations:
  • 1.Finite-difference method, (convergence and stability of difference schemes).
  • 2.Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 MS1,01016
  • Timetable of Seminar Groups:
M9100/01: Tue 14:00–14:50 MS1,01016, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
The most important methods for solving initial-value and boundary-value problems are introduced.
Particular methods are not only described from the theoretical point of view, but they are also reviewed from the point of view of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • Methods for solving partial differential equations:
  • 1.Finite-difference method, (convergence and stability of difference schemes).
  • 2.Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods
lectures,class exercises,
oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2007
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 UP1
  • Timetable of Seminar Groups:
M9100/01: Mon 12:00–12:50 UP1, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2006
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Wed 10:00–11:50 UP1
  • Timetable of Seminar Groups:
M9100/01: Wed 12:00–12:50 UP1, L. Adamec
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Tue 7:00–8:50 N41
  • Timetable of Seminar Groups:
M9100/01: Tue 9:00–9:50 M3,04005 - dříve Janáčkovo nám. 2a, J. Zelinka
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2004
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Mon 9:00–10:50 B011
  • Timetable of Seminar Groups:
M9100/01: Mon 13:00–13:50 UM, J. Zelinka
Prerequisites
M4180 Numerical methods I && M5180 Numerical Methods II
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable of Seminar Groups
M9100/01: No timetable has been entered into IS. J. Zelinka
Prerequisites
M4180 Numerical methods I && M5180 Numerical Methods II
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer), Mgr. Jiří Zelinka, Dr. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer), Mgr. Jiří Zelinka, Dr. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites (in Czech)
( M5122 Numerical Methods II || M6122 Numerical Methods II ) && ( M5160 Differential Eqs.&Cont. Models || M6160 Differential Eqs.&Cont. Models ) && M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Cauchy initial problem,Runge- Kutta methods for ordinary differential equations,multistep methods
Variational methods,Ritz method, Galerkin method
Finite elements methods for partial differential equations
Finite difference methods for partial differential equations
Shooting methods for boundary value problem
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
Assessment methods (in Czech)
Zkouška ústní
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2000
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer), Mgr. Jiří Zelinka, Dr. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Cauchy initial problem,Runge- Kutta methods for ordinary differential equations,multistep methods
Variational methods,Ritz method, Galerkin method
Finite elements methods for partial differential equations
Finite difference methods for partial differential equations
Shooting methods for boundary value problem
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
Assessment methods (in Czech)
Zkouška ústní
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 1999
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer), Mgr. Jiří Zelinka, Dr. (deputy)
Mgr. Jiří Zelinka, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites (in Czech)
M5122 Numerical Methods II && M5160 Differential Eqs.&Cont. Models && M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus
  • Cauchy initial problem,Runge- Kutta methods for ordinary differential equations,multistep methods
  • Variational methods,Ritz method, Galerkin method
  • Finite elements methods for partial differential equations
  • Finite difference methods for partial differential equations
  • Shooting methods for boundary value problem
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
Assessment methods (in Czech)
Zkouška ústní
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2023

The course is not taught in Autumn 2023

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Learning outcomes
Student will be able to:
- numerical solving of ordinary differential equations - initial and boundary value problem - using computers
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2022

The course is not taught in Autumn 2022

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Learning outcomes
Student will be able to:
- numerical solving of ordinary differential equations - initial and boundary value problem - using computers
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
autumn 2021

The course is not taught in autumn 2021

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Learning outcomes
Student will be able to:
- numerical solving of ordinary differential equations - initial and boundary value problem - using computers
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2020

The course is not taught in Autumn 2020

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Learning outcomes
Student will be able to:
- numerical solving of ordinary differential equations - initial and boundary value problem - using computers
Syllabus
  • 1. Introduction: The solvability of differential equations, approximate solutions, error, stability.
  • 2. One-step methods: Euler method, Taylor series method, Runge-Kutta methods
  • 3. Multistep methods: Adams methods, predictor-corrector
  • 4. Boundary value problems: shooting method, method of differences
  • 5. Variational methods: Ritz method, Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures, class exercises
Assessment methods
Oral examination with preparation.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • 2.Variational methods for solving ordinary differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving ordinary differential equations

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course gives a survey of methods for numerical solving of differential equations (ordinary and partial).
Students will acquire the most important methods for solving initial-value, boundary-value problems for ordinary differential equations.
At the end of this course, students will be able to compare the methods not only from the theoretical point of view, but they will understand them from the point of stability, efficiency, etc.
Syllabus
  • Methods for solving ordinary differential equations :
  • 1.Initial-value problems (Runge-Kutta methods, multistep methods).
  • 2.Boundary-value problems (shooting method, difference methods)
  • 2.Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Teaching methods
Lectures,class exercises
Assessment methods
Oral examination.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.

M9100 Numerical methods for solving differential equations

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Basis of functional analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The solving of large technical and scientific problems can be often modeled by means of differential equations.Practical solving of such problems consists in application of suitable numerical method. This course aims to give a survey of methods for numerical solving of differential equations.The most important methods for solving of initial-value and boundary-value problems for ordinary equations and methods for partial differential equations are introduced. Particular methods are not only described from the theoretical point of view,but they are also reviewed from the point of view of stability,efficiency ,etc.The practical examples indicate the possible characteristic difficulties in applications.
Syllabus
  • Variational methods for solving ordinary and partial differential equations:Ritz method,Galerkin method. Methods for solving ordinary differential equations : 1.Initial-value problems (Runge -Kutta methods,multistep methods). 2.Boundary-value problems (shooting method,difference methods) Methods for solving partial differential equations: Finite -difference method,convergence and stability of difference schemes.
Literature
  • VITÁSEK, Emil. Základy teorie numerických metod pro řešení diferenciálních rovnic. 1. vyd. Praha: Academia, 1994, 409 s. ISBN 8020002812. info
  • BABUŠKA, Ivo and Milan PRÁGER. Numerické řešení diferanciálních rovnic (Numerical solution of differential equations). 1st ed. Praha: Státní nakladatelství technické literatury, 1964, 238 pp. info
  • REKTORYS, Karel. Metoda časové diskretizace a parciální diferenciální rovnice. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 361 s. URL info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Assessment methods (in Czech)
Přednáška,cvičení částečně v počítačové učebně. Zkouška :ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
General note: Pro zapsání předmětu je třeba zná tzákladní numerické metody matematické analýzy a lineární algebry a základy funkcionální analýzy.
The course is also listed under the following terms Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.
  • Enrolment Statistics (recent)