Which tool can I use to solve the nonlinear pde system with three functions?

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I have three nonlinear equations with three unknown functions as attached. Which tool will be more useful and easier to solve this nonlinear pde system using finite difference? Thanks.

Accepted Answer

Tushar Athawale
Tushar Athawale on 4 Jan 2016
The following link refers to types of problems you can solve using MATLAB PDE toolbox:
MATLAB "pdepe" function can be used to solve initial-boundary value problems for parabolic-elliptic PDEs in 1-D:

More Answers (1)

Hasti on 1 Feb 2019
I have a similar system of nonlinear PDEs where I have an extra time-derivative in one equation (the same as eqautin (1c) in the attached file for the original question nonlinear_wake.pdf). Can "pdepe" solve these system of equations? If yes, how? (because I did not see it in the definition of pdepe in matlab) and if not which other method do you suggest?
Thank you very much.

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