On Mon, May 27, 2013 at 12:14 PM, F. B. <franz.bona...@gmail.com> wrote: > Generic Partial Differential Equations may yield arbitrary functions in > their solutions. > > When matching this generic solutions to initial or boundary conditions, we > get a functional equation: that is an equation whose variable is a function > (without derivatives). > > If the function to be found has the same parameters everywhere, that case > reduces to a simple equation. If the parameters are different, that can be > very complicated to deal. > > Which case is the better one: > > Given a PDE and initial/final/boundary conditions, implement an algorithm > which finds the solution without passing through the generic arbitrary > function solution. > Find the general solution of the PDE, then solve a functional equation to > match the initial/boundary conditions. > > I don't know very much theory about general functional equation solving, is > there any idea? > > Maybe a functional equation solver may be useful even outside of PDE > solvers?
Yes, I think it would, and we should implement it. Even so, if there are PDE hints that can bypass the whole thing, that is fine too. The philosophy of the ODE and PDE modules is to implement various types of hints, even ones that can solve the same equations, and try to pick the best one by default, but also give the user the opportunity to try different ones. Aaron Meurer -- 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 sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
