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Coupled Differential Equation

조회 수: 4 (최근 30일)
Graig
Graig 2011년 4월 21일
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
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Jarrod Rivituso
Jarrod Rivituso 2011년 4월 21일
Forgive me if I misunderstand, but are you not using one of the ODE solvers?
Graig
Graig 2011년 4월 21일
No, I was not using ODE solution. I am not sure, whether I can use ODE for such a high number of differential equation. Will glad to know about it.

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채택된 답변

Andrew Newell
Andrew Newell 2011년 4월 26일
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).

추가 답변 (3개)

Jarrod Rivituso
Jarrod Rivituso 2011년 4월 21일
I would recommend giving these a try:
I've never used them with the number of states you have. You may end up finding that your system is "stiff", depending on the system dynamics. In this case, you may prefer ode15s or other stiff solvers to the commonly used ode45.

Graig
Graig 2011년 5월 2일
Thanks guys. But I don't know how to put this solver in a loop. Need to think about it.
  댓글 수: 7
Andrew Newell
Andrew Newell 2011년 5월 4일
This question is starting to sprawl and it is not clear what is going on. I recommend you accept an answer for this question and submit a new one in which you show us the code you used and describe the problem you are having.
Graig
Graig 2011년 5월 5일
Above that I meant 't_final'. I could solve the equation when I am limited to TSPAN = [0 1.0E-6] when the other parameters e.g., gamma and so on are set to some value. If I increase the final time, meaning 1.0E-6 to say 1.0E-4 it went to the error message. I am bound to keep the input parameters (gamma, P etc) fix. Physically this should work for all time interval.

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Graig
Graig 2011년 5월 5일
Here is a discussion I found recently on this topic.

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