# How can I solve simultaneous PDEs using pdepe?

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Shrishti on 8 Oct 2013
I have a set of two pdes that are interlinked. How do I use pdepe to solve the two equations simultaneously?

Jie on 8 Oct 2013
I'm afraid matlab may not be able to solve coupled(interlinked) PDEs with its own pdepe function. I used that one before. However, you could always do it yourself if you could apply some numercial methods and encode yourself with soooo powerful matlab. I'd like to recommend you a software call COMSOL. It was a matlab pde toolblx and later seperated from matlab and it is dedigned to solve coupled PDEs.

Bill Greene on 8 Oct 2013
By "two pdes that are interlinked" do you mean that you have two PDE and two dependent variables, say, u1 and u2?
If so, pdepe can definitely solve systems of this type. Take a look at example 2 on this page:
pdepe can handle systems with any reasonable number of partial differential equations.
If you have a different type of PDE system in mind, please provide more information and we may be able to point you in the right direction.
Bill

Jacob on 5 Jun 2014
Edited: Jacob on 5 Jun 2014
I have a similar question (I think).
Can the pdepe tool solve coupled pde's?
The example on the link you sent has a vector of coefficients for the f function that depend on DuDx. Can I enter Du(1)Dx and Du(2)Dx? Below is the general form of the equations:
d(u1)/dt = d/dx (d(u1)/dx - d(u2)/dx))
d(u2)/dt = d/dx (d(u2)/dx - d(u2)/dx))
Muhammad Hashim Khan on 15 Apr 2021
I know Its quite a bit late but for anybody ready yes it is possible to solve couple pdes using pdepe.