Dear Oscar, Just for my understanding:
Why do you feel, it would be useful for sympy to be able to numerically solve ordinary differential equations? Scipy seems to have very good routines to do this - or am I wrong, and they are not as good as I think? Thanks! Peter On Thu 17. Mar 2022 at 04:21 Oscar Benjamin <[email protected]> wrote: > 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 > . > -- Best regards, Peter Stahlecker -- 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/CABKqA0ay7cTqnoALWwpAavcxCip88ss6EsMxaPjnbiwfoUcimg%40mail.gmail.com.
