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

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Meva
Meva 2015-12-31
回答： Hasti 2019-2-1
Hello,
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.

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Tushar Athawale
Tushar Athawale 2016-1-4
The following link refers to types of problems you can solve using MATLAB PDE toolbox:
http://www.mathworks.com/help/pde/ug/types-of-pde-problems-you-can-solve.html
MATLAB "pdepe" function can be used to solve initial-boundary value problems for parabolic-elliptic PDEs in 1-D:
http://www.mathworks.com/help/matlab/ref/pdepe.html

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Hasti
Hasti 2019-2-1
Hello,
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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