How to solve a system of n differential equations?
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Marlon Saveri Silva
le 31 Mar 2018
Commenté : Walter Roberson
le 31 Mar 2018
Hello everyone, I got the solution below from the help, I tried an example with a 3x3 system and it runs ok. However, when I try to apply it to my real system, I can not find an answer. Do you have any idea why?
Example:
syms x(t) y(t)
A = [1 2; -1 1];
B = [1; 1];
Y = [x; y];
odes = diff(Y) == A*Y + B;
C = Y(0) == [2; -1];
[xSol(t), ySol(t)] = dsolve(odes,C);
My problem:
clear; close 'all'; clc;
syms T1(t) T2(t) T3(t) T4(t) T5(t)
syms x(t) y(t) z(t) w(t) p(t)
A = [-81 1 0 0 0
0.5 -0.56 0.02 0.04 0
0 0.004 -0.008 0.004 0
0 0.267 0.13 -1.4 1
0 0 0.273 3 -82.1];
B = [24000;0;0;1.333;6300];
Y = [x; y; z; w; p];
odes = diff(Y) == A*Y + B;
C = Y(0) == [300; 300; 300; 300; 300];
[xSol(t), ySol(t), zSol(t), wSol(t), pSol(t)] = dsolve(odes,C);
2 commentaires
Walter Roberson
le 31 Mar 2018
R2018a finds a solution. It does, however, depend upon an arbitrary constant of integration, which would tend to suggest that dsolve thinks there should be one more initial condition.
Réponse acceptée
Star Strider
le 31 Mar 2018
You appear to have a dynamic system. The Control System Toolbox would be more appropriate.
One way to solve it would be to convert it to an anonymous function and solve it with ode45:
[VF,Subs] = odeToVectorField(odes)
Sys = matlabFunction(VF,'Vars',{'t','Y'})
Y0 = [300; 300; 300; 300; 300];
[T,Y] = ode45(Sys, [0 5], Y0);
figure(1)
plot(T,Y)
grid
lgnd = regexp(sprintf('%s\n',Subs), '\n', 'split');
legend(lgnd(1:end-1), 'Location','E')
5 commentaires
Star Strider
le 31 Mar 2018
Not that I’m aware of.
You can try something like this, although you would then have to manually copy the output and paste it to your syms call (without the single quotes):
TV = sprintf('T%d(t) ', 1:10)
TV =
'T1(t) T2(t) T3(t) T4(t) T5(t) T6(t) T7(t) T8(t) T9(t) T10(t) '
I know of no way to do it programmatically.
Walter Roberson
le 31 Mar 2018
You posted a solution in https://www.mathworks.com/matlabcentral/answers/391756-how-to-declare-time-dependent-symbolic-array#answer_312845 and I posted a one-line solution in https://www.mathworks.com/matlabcentral/answers/222866-time-dependence-array-in-dae-symbolic-math-toolbox#comment_551734
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