MA030 Numerical Differencial Equation Solving I

Faculty of Informatics
Autumn 2004
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
Mgr. Jiří Zelinka, Dr. (lecturer), Mgr. Jiří Zelinka, Dr. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Mon 9:00–10:50 B011, Mon 11:00–11:50 B011
  • Timetable of Seminar Groups:
MA030/01: No timetable has been entered into IS. J. Zelinka
Prerequisites
! M030 Numerical Differencial Equation Solving I
Knowledge of basic numerical methods of mathematical analysis and linear algebra is supposed. Principles of functional analysis are needed in the first part.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
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
  • Numerical solution of Cauchy problem of ordinary differential equations.
  • Runge-Kutta methods, multistep methods.
  • Numerical solution of boundary value problems of partial differential equations and of equations in Hilbert spaces.
  • Finite difference methods, Rayleigh-Ritz method, Galerkin method, method of lines, finite elements.
  • Stability and convergence of numerical methods.
Literature
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
  • BARTUŠEK, Miroslav. Numerické metody řešení diferenciálních rovnic. [1. vyd.]. Praha: Rektorát UJEP, 1975, 92 s. info
  • RALSTON, Anthony. Základy numerické matematiky. 1. české vyd. Praha: Academia, 1973, 635 s. URL info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2004/MA030