Solving coupled ODEs with Matlab

[mika]

I was wondering how coupled ODEs could be solved with Matlab.. I'm having trouble passing the coupling solution vectors between solvers since the length of the vectors isn't constant during the iteration e.g.

sol1 = bvpinit(linspace(0.,h,200),[0.1 0]);
sol2 = bvpinit(linspace(0.,h,200),@mat4init);

f=sol1.y
g=sol2.y

sol1 = bvp4c(@fODE,@fBC,sol1,options1,g,Re,K);
sol2 = bvp4c(@gODE,@gBC,sol2,options1,f,Re,K);


function dydx = fODE(x,y,g,Re,K)

dydx = [ y(2,:)
Re*(y(1,:).^2-g.*2+K^2)];

function dgdx = gODE(x,y,g,Re,K)

dgdx = [ g(2,:)
2*Re*(y(1,:).*g(1,];

this doesn't work bacause the dimensions of y and g don't match during iteration. Any ideas how to overcome this?

 

[Aaron Barnard]

The best way to solve coupled ODEs with Matlab is to use the built-in function bvp4c. This function allows you to pass a second parameter (in addition to the ODE and boundary condition) containing the values of the other equation that need to be used in the current iteration. For example, if you have two coupled ODEs, you can call bvp4c like this:

sol1 = bvp4c(@fODE,@fBC,sol1,options1,g,Re,K);
sol2 = bvp4c(@gODE,@gBC,sol2,options1,f,Re,K);

where f and g are the solution vectors from the previous iteration, and Re and K are parameters for both equations. The bvp4c function will then take care of passing the correct values between the two equations.

 

[raining Pete]

Hi there,

I've encountered a similar issue before when solving coupled ODEs with Matlab. One thing you can try is to use the "events" option in the bvp4c solver to specify a specific event that will trigger a change in the length of the vectors. For example, you can set an event that checks if the length of the vectors has reached a certain value and if so, it will trigger a change in the initial conditions for the next iteration. You can also try using a "while" loop to continuously update the initial conditions until the desired length is reached.

Another approach you can try is to use the "ode15s" solver instead of bvp4c. This solver is specifically designed for stiff systems of ODEs and may handle the changing length of the vectors better.

I hope this helps. Let me know if you have any other questions or if these suggestions work for you. Good luck with your problem!