Obtain the analytic solution of a system of PDEs

Hi people.

I have a 2nd order linear system of PDEs, with additional free parameters. I can solve this using MATLAB's pdepe function and obtain a numeric solution when I give values to the free parameters, but I would like the analytic solution as a function of those. How can I do this? I can obtain the analytic solution of ODEs by specifying them along with my variables:

syms param1 param2 param3 u(t) v(t)

But, solving PDEs using pdepe uses a different procedure, for which I can't figure out how to specify and solve with free parameters. Thanks!

[Xen]

Anyone?!

Answer 1

[Torsten]

There is no tool in MATLAB for the analytical solution of PDEs analogous to "dsolve" for ODEs.

Best wishes

Torsten.

[Torsten]

How complex is your PDE ? Could you post the equation(s) ?

Best wishes

Torsten.

[Torsten]

A = B = 0 is a solution :-)

You see: No existing software package will be able to give the general solution to such a general system of PDEs (without specifying boundary and initial conditions).

You may want to try MATHEMATICA for free available under

www.wolframalpha.com

or consult a textbook

https://www.amazon.com/Handbook-Differential-Equations-Engineers-Scientists/dp/146658145X/ref=sr_1_5?s=books&ie=UTF8&qid=1517917346&sr=1-5&keywords=polyanin

But my advice is: Stick to numerical solvers (like pdepe).

Best wishes

Torsten.