Wolfram Mathematica has RSolve: http://reference.wolfram.com/mathematica/ref/RSolve.html
It is mainly used to solve recurrence equations, though it is able to accept functional equations too. Wikipedia on recurrence equations: http://en.wikipedia.org/wiki/Recurrence_relation On Monday, May 27, 2013 7:32:39 PM UTC+2, Aaron Meurer wrote: > > On Mon, May 27, 2013 at 12:14 PM, F. B. <franz....@gmail.com <javascript:>> > 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.
