GSoC 2015 Application : Improved PDE solver.

[Darshan Chaudhary]

Greetings everyone !

I am Darshan Chaudhary and am pursuing my B.E.(Hons.) from BITS Pilani, Hyd Campus India. I have been active in the SymPy community since the last 2 months. For my GSoC project, I chose to work on the Partial Differential Equations module in SymPy which was started by Manoj Kumar in 2013 but hasn't seen much development since. Currently, it can only handle the most basic 1st order linear PDEs. I propose to extend the functionality of the solver by implementing the Method of Characteristics which will enable it to also solve semi-linear and quasilinear 1st order PDEs.

Also, I plan on adding the ability to classify 2nd order PDEs into Parabolic, Hyperbolic or Elliptic. This classification will serve as the bedrock on which the future endeavor of solving the equations will rest.

I have prepared the first draft of the application : https://github.com/sympy/sympy/wiki/GSoC-2015-Application-:-Darshan-Chaudhary-Improved-PDE-Solver

Kindly review and provide comments/suggestions

Thanks !