MATLAB: Coupled Differential Equation

Question

Dear Friend,

I am solving a coupled differential equation in matlab to simulate the laser rate equation. The number of differential equation depends on the number of modes I will put through input, usually it is a very high number say 500-600.

I have two for loops inside another for loop.

I use the usual trick: dx/dt = Ax (say this is the differential equation)

so x2 = x1 + dt(Ax) (I solve it this way giving an initial condition on x1)

The problem is, this equation will be valid as long as abs(dx/x)<<1. And we need 'dt' for this purpose very small, which will eventually increases the iteration of my for loop. Now when I do that, I got an out of memory error.

Is there a way to get rid of it. I was thinking of extracting few outputs from the iteration (not all the output), but also it didn't work.

Thanks for your time.

-Graig

Answer 1

Here is an example where someone is using ode45 to solve an even bigger problem. To avoid out-of-memory errors, make A into a sparse matrix if you can.

EDIT: If I understand your notation, M is actually a vector with components M_q, and ditto for K and B. So you should create a new vector

X = [M; N];

and then define your function as follows:

f = @(x) [-gamma*x(1:end-1) + x(end)*B.*(x(1:end-1)+1) - c*K.*x(1:end-1); P - A*x(end) - x(end)*sum(B.*x(1:end-1))];

(or you could create an easier-to-read function in a separate file).