(1.1)(1.1)
(1.2)(1.2)
Zero Order
restart;with( DEtools ):with( plots ):with (linalg):
ode_1:=diff(ca(t),t)=-k_1;ode_2:=diff(cb(t),t)=(k_1);
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=cb0},cb(t));
sol:= dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0},{ca(t),cb(t)})
;
k_1:=1:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=0}, type=
numeric, output=listprocedure);#assign(nsol);f:=eval(ca(t),
sol);f(t=1);
nsol(1);
odeplot(nsol,[[t,ca(t)],[t,cb(t)]],0..1,labels=[t,c],legend=
[c_A,c_B],thickness=3);
c_A c_B
t
0 1
c
0
1
Prvniho radu A ->B
restart;with( DEtools ):with( plots ):with (linalg):
ode_1:=diff(ca(t),t)=-k_1*ca(t);
ode_2:=diff(cb(t),t)=(k_1)*ca(t);
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=cb0},cb(t));
(2.1)(2.1)
sol:= dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0},{ca(t),cb(t)})
;
k_1:=1:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=0}, type=
numeric, output=listprocedure);#assign(nsol);f:=eval(ca(t),
sol);f(t=1);
nsol(1);
odeplot(nsol,[[t,ca(t)],[t,cb(t)]],0..5,labels=[t,c],legend=
[a,b],thickness=3);
a b
t
0 1 2 3 4 5
c
0
1
Reakce druheho radu 2A->B
restart;with( DEtools ):with( plots ):with (linalg ):
ode_1:=diff(ca(t),t)=-k_1*(ca(t))^2;
ode_2:=diff(cb(t),t)=(k_1)*(ca(t))^2;
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=ca0},cb(t));
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0},{ca(t),cb(t)});
k_1:=1:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=0}, type=
numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)]],0..80,labels=[t,c],legend=
[a,b],thickness=3);
(4.1)(4.1)
a b
t
0 10 20 30 40 50 60 70 80
c
0
1
Reakce druheho radu A+B->C
restart;with( DEtools ):with( plots ):with (linalg ):
ode_1:=diff(ca(t),t)=-k_1*(ca(t))*(cb(t));
ode_2:=diff(cb(t),t)=-k_1*(ca(t))*(cb(t));
ode_3:=diff(cc(t),t)=k_1*(ca(t))*(cb(t));
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=ca0},cb(t));
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0,ode_3,cc(0)=cc0},{ca
(t),cb(t),cc(t)});
k_1:=1:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=.1,ode_3,cc
(0)=0}, type=numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)],[t,cc(t)]],0..80,labels=[t,
c],legend=[a,b,c],thickness=3);
a b c
t
0 10 20 30 40 50 60 70 80
c
0
1
Srovnání prvního a druhého ádu
restart;with( DEtools ):with( plots ):with (linalg):
ode_1:=diff(ca(t),t)=-k_1*ca(t);
ode_2:=diff(cb(t),t)=-(k_1)*(cb(t))^2;
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=cb0},cb(t));
sol:= dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0},{ca(t),cb(t)})
;
(5.1)(5.1)
k_1:=log(2):nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=1},
type=numeric, output=listprocedure);#assign(nsol);f:=eval(ca
(t), sol);f(t=1);
%nsol(1);
odeplot(nsol,[[t,ca(t)],[t,cb(t)]],0..5,labels=[t,c],legend=
[prvního,druhého],thickness=3);
prvního druhého
t
0 1 2 3 4 5
c
Paralelni reakce A->B,A->C
restart;with( DEtools ):with( plots ):with (linalg ):
ode_1:=diff(ca(t),t)=-(k_1+k_2)*ca(t);
ode_2:=diff(cb(t),t)=(k_1)*ca(t);
ode_3:=diff(cc(t),t)=(k_2)*ca(t);
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0,ode_3,cc(0)=cc0},{ca
(t),cb(t),cc(t)});
dsolve({ode_2,cb(0)=cb0},cb(t));
k_1:=1.8:k_2:=2:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=0,
ode_3,cc(0)=0}, type=numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)],[t,cc(t)]],0..2,labels=[t,
c],legend=[a,b,c],thickness=3);
a b c
t
0 1 2
c
0
1
Nasledne reakce
restart;with( DEtools ):with( plots ):with (linalg):
ode_1:=diff(ca(t),t)=-k_1*ca(t);
ode_2:=diff(cb(t),t)=k_1*ca(t)-k_2*cb(t);
ode_3:=diff(cc(t),t)=k_2*cb(t);
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=cb0},cb(t));
dsolve({ode_3,cc(0)=cc0},cc(t));
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0,ode_3,cc(0)=cc0},{ca
(t),cb(t),cc(t)});
k_1:=1:k_2:=5:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=0,
ode_3,cc(0)=0}, type=numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)],[t,cc(t)]],0..5,labels=[t,
c],legend=[a,b,c],thickness=3);
a b c
t
0 1 2 3 4 5
c
0
1
Vratná reakce A <--> B
restart;with( DEtools ):with( plots ):with (linalg):
ode_1:=diff(ca(t),t)=-k_1*ca(t)+k_2*cb(t);
ode_2:=diff(cb(t),t)=(k_1)*ca(t)-k_2*cb(t);
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=cb0},cb(t));
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0},{ca(t),cb(t)});
k_1:=5:k_2:=4:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=.5},
type=numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)]],0..1,labels=[t,c],legend=
[a,b],thickness=3);
a b
t
0 1
c
ešení využívající piblížení
Reakce druheho ádu A+B->C, pevedená na pseudoprvní ád
(9.1.1)(9.1.1)
restart;with( DEtools ):with( plots ):with (linalg ):
ode_1:=diff(ca(t),t)=-k_1*(ca(t))*(cb(t));
ode_2:=diff(cb(t),t)=-k_1*(ca(t))*(cb(t));
ode_3:=diff(cc(t),t)=k_1*(ca(t))*(cb(t));
dsolve({ode_1,ca(0)=ca0},ca(t));
dsolve({ode_2,cb(0)=ca0},cb(t));
dsolve({ode_1,ca(0)=ca0,ode_2,cb(0)=cb0,ode_3,cc(0)=cc0},
{ca(t),cb(t),cc(t)});
k_1:=1:nsol := dsolve({ode_1,ca(0)=1,ode_2,cb(0)=100,ode_3,
cc(0)=0}, type=numeric);
odeplot(nsol,[[t,ca(t)],[t,cb(t)],[t,cc(t)]],0..0.1,labels=
[t,c],legend=[a,b,c],thickness=3);
a b c
t
0
c
0
20
40
60
80
100
odeplot(nsol,[[t,ca(t)]],0..0.1,labels=[t,c],legend=[a],
thickness=3);
a
t
0
c
0
1
odeplot(nsol,[[t,cb(t)]],0..0.1,labels=[t,c],legend=[b],
thickness=3,color=[green]);
b
t
0
c
99
100