Solving Boundary Value Problem in 2D

I am trying to solve the 2D boundary value problem (energy equation for non-isothermal flow of non-newtonian fluids) inside a channel with rectangular cross-section. One version of that equation looks e.g. like this: a.dT/dx=d^2T/dy^2+b.exp(-T) Do the existing capabilities of Matlab offer a way for solving a BVP of this type without programming a finite difference code?

Answer 1

[Torsten]

Interpret x as time(t) and y as length(x) and use MATLAB's "pdepe".

Best wishes

Torsten.

[Saeid]

Danke Torsten. I didn't know that such function exists. Is there a chance you have some examples that you can share? Saeid

[Torsten]

Here are some examples:

https://de.mathworks.com/help/matlab/ref/pdepe.html#f93-998895

Maybe the MATLAB documentation contains some more.

Best wishes

Torsten.