# Solving a complex system of differential equations

6 views (last 30 days)
Ali Almakhmari on 15 Nov 2023
Commented: Torsten on 15 Nov 2023
I have a this differential equation system: , where F is a function of time (t). But I am not sure whats the easiest way to solve it in MATLAB. Lets say for example:
M = [1,0.8;0.8,7]
K = [5,0;0,10]
D = [0.15,0;0,0.35]
F = [5*exp(i*5*t); 3.65*exp(i*5*t)]
q = [X; Y]
And we want to solve for q, which is X and Y.

Torsten on 15 Nov 2023
Edited: Torsten on 15 Nov 2023
%q(1) = X, q(2) = Y, q(3) = Xdot, q(4) = Ydot
M = [1,0.8;0.8,7];
K = [5,0;0,10];
D = [0.15,0;0,0.35];
F = @(t)[5*exp(i*5*t); 3.65*exp(i*5*t)] ;
tspan = [0 1];
q0 = [0 1 1 0].';
fun = @(t,q)[[q(3);q(4)];inv(M)*(F(t)-(1i*D+K)*[q(1);q(2)])];
[T,Q] = ode45(fun,tspan,q0);
figure(1)
hold on
plot(T,real(Q(:,1)))
plot(T,imag(Q(:,1)))
hold off
figure(2)
hold on
plot(T,real(Q(:,2)))
plot(T,imag(Q(:,2)))
hold off
Ali Almakhmari on 15 Nov 2023
Is the first plot for q(1) and q(2) or is it for q(3) and q(4)? Because the definition of fun makes me think its q(3) and q(4)
Torsten on 15 Nov 2023
The first plot is for the real and imaginary part of q(1) = X, the second plot is for the real and imaginary part of q(2) = Y.
q(3) and q(4) are Xdot and Ydot, respectively (as written in the headline of the code).

### Categories

Find more on Graphics Performance in Help Center and File Exchange

R2022b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!