MATLAB Answers

Solve system of differential equations with vector input

8 views (last 30 days)
Xen
Xen on 14 Jan 2020
Commented: Star Strider on 15 Jan 2020
Assume that I want to solve the system of equations below for u and v. A and B are known numbers (say, 1 and 2 respectively) and a(t) is a fixed vector that I want to pass to the solution and get the result. How can I do it? The code works fine when a(t) is not used.
syms A B u(t) v(t) a(t)
ode1 = diff(u,t) == A * (a - u);
ode2 = diff(v,t) == B * (u - v);
odes = [ode1; ode2];
[uSol(t), vSol(t)] = dsolve(odes);
% Above work fine; below don't
uF = matlabFunction(uSol);
vF = matlabFunction(vSol);
resultu = uF(0:10, 1, 2); % t, A, B
resultv = vF(0:10, 1, 2);

  0 Comments

Sign in to comment.

Accepted Answer

Star Strider
Star Strider on 14 Jan 2020
In the derivation, let ‘a’ simply be an undefined constant, and define the initial conditions as 0 (unless you want them to be something else). Then in the solution, provide ‘a’ as a row vector to get the solution:
syms A B u(t) v(t) a
ode1 = diff(u,t) == A * (a - u);
ode2 = diff(v,t) == B * (u - v);
odes = [ode1; ode2];
[uSol(t), vSol(t)] = dsolve(odes, u(0)==0, v(0)==0)
% Above work fine; below don't
uF = matlabFunction(uSol);
vF = matlabFunction(vSol);
av = randn(1, 11);
resultu = uF(0:10, 1, 2, av); % t, A, B
resultv = vF(0:10, 1, 2, av);
This evaluates them as functions of whatever you want to define ‘a’ to be.

More Answers (0)

Sign in to answer this question.