On Tue, 15 Mar 2022 at 08:51, KSHITIJ SONI 19PE10041 <[email protected]> wrote: > > Hey! > > I went through all the SymPy ideas, I also mailed Aaron regarding my interest > in Risch Algorithm. But as GSoC allow open ideas. I would like to take up the > task of solving PDEs. > > To start with we can develop : > 1. Lagrange's Equation > 2. Charpit's method > > I think that within 350 hr constraint these two methods can be developed and > improvised. After the GSoC timeline, I would like to add Non-Linear First > order equations, higher-order linear equations with constant coefficients, > quasi-linear second-order equations ( Monge's method). > > Partial Differential Equations have enormous applications, if we can > introduce this module we can take it forward with SymPy. PDEs has the > capability to have software of their own.
While PDEs do have enormous applications the vast majority of work with them is numeric rather than symbolic and there are clear reasons for that. It's really not clear to me if it is even possible to define a meaningful subset of PDEs that can be handled purely analytically in a systematic way. Various methods for PDEs are commonly taught in various courses and textbooks but few of them actually stand up when applied to problems that are not contrived. Speaking as someone who has taught such things I can tell you that the examples that are used (in lectures, books and exams) are selected very carefully. That's because there is an extremely thin line between problems that are totally trivial and the problems where some or other method theoretically applies but is completely intractable and fails in practice. Charpit's method is a good example where exam questions are recycled not out of laziness but necessity: there are really only a handful of problems that you could ever pose for it. I'm not convinced that it is useful to add functionality for this sort of thing to SymPy. Certainly it is not a priority right now. A more useful way to go with PDEs is probably something like making use of symbolics to complement or facilitate numerical applications. SymPy currently lacks even the capability to numerically solve ODEs though and that's far more important: https://github.com/sympy/sympy/issues/18023 -- Oscar -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxTxzeqGcqE_a0-S3rEz-0YQzzg63ZvF6k6Cy2Tz0u2o%3DQ%40mail.gmail.com.
