Can PDEPE solve 1-D Nonlinear PDE equation systems well?

Hi, I recently have to solve these PDEs as shown below

I tried PDEPE, it doesn't work. So I'm wondering whether give PDE toolbox a try as it aims to 2-D and 3-D PDEs. Could anybody give me some suggestions on solving that using matlab solver? Thanks a lot!

Regards,

Yi

Answer 1

[Torsten]

If pdepe does not succeed, the toolbox also won't succeed for this 1-d problem.

Show us your code - maybe we can find the reason that pdepe fails.

Best wishes

Torsten.

[Yi chen]

Thank you Torsten for the reply.

The code I tried PDEPE is attached.

I hope you can help me to figure it out.

Yi

[Torsten]

I suspect that boundary conditions and source terms are simplifications of what had to be set to be consistent with your PDEs. This might cause problems for pdepe. What error message do you get ?

One hint: Multiply all three equations by V_xm^2 and put this factor in the c-array.

Best wishes

Torsten.

[Yi chen]

I don't get any error message when I run the code, matlab seems dead there, no"busy" notice shown in the left corner.

I tried your hint, it makes the s-array simple, that's great! I also ran it, the same issue with the original one.

I don't understand what you said "I suspect that boundary conditions and source terms are simplifications of what had to be set to be consistent with your PDEs.". could you explain more? I didn't know why boundary conditions can affect the solver running here.

I attach the modified code here, you can try to see is there any error message pop out.

Thank you again for your help!

Yi

[Torsten]

Just a question concerning the background of your model:

Why don't you just solve the first two PDEs and deduce xa from the condition

xa=1-x1-xm ?

Best wishes

Torsten.