Second Order PDE Solvers

[Karl Deutscher]

Hi to all who read this,

I know that the topic of second order PDE solvers has already been discussed in this forum but I thought that I would raise it again because I didn't see anything showing it had been resolved. I am currently taking a degree in mathematics with a minor in computer science and am enrolled in an introductory PDE course this term. I noticed that the pde solver as it currently stands only solves first order linear PDEs. I am wondering if it would be of help if I tried to implement a solver for second order linear PDEs that are of hyperbolic, elliptic and parabolic classifications. As a result the classify_pde would also be updated to classify a second order linear PDE. If this is successful I could also try to use the Fourier series  or other methods to solve second order linear PDEs and heat and wave equations. The algorithms would be theoretical as that is how I am being taught PDEs so as a result the solutions would not be numerical unless I run into  issues with the theoretical side. I have not yet done any patches for sympy and so I am unsure if that is required before I can dig into implementing code in a module.

From,

Karl Deutscher

[Jason Moore]

Karl,

That sounds like a great idea. I think you'd only want to implement analytical methods in SymPy. There are likely other options for numerical PDE solvers.

See this to get started: https://github.com/sympy/sympy/wiki/introduction-to-contributing

Jason
moorepants.info
+01 530-601-9791

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[Aaron Meurer]

I think it would be great to be able to solve more kinds of PDEs. It
would have helped when I took similar courses in college.

If you feel comfortable jumping right in then jump right in. If you
are unsure, you can start with an easier issue. There are no
requirements that you do one thing before you do another thing with
respect to contributing. There are generic guidelines for
contributing (see
https://github.com/sympy/sympy/wiki/Introduction-to-contributing and
https://github.com/sympy/sympy/wiki/Development-workflow), for
example, all new code needs to have tests. But if you miss anything
we'll let you know when you submit a pull request.

Aaron Meurer

[Karl Deutscher]

Ok thanks, I will start digging in at the problem then and will hopefully have some of it ready soon.

[Karl Deutscher]

I have approached a professor at my university that specializes in PDEs and he is interested in discussing this topic with me. I will post again after he and I have spoken.

[Karl Deutscher]

I have spoken with my professor and we plan to work on this issue over the summer.