Foad S Farimani wrote: > > While ago I was trying to use polynomial power series to solve a system of > partial differential and algebraic equations, when realized there is no > implementation of the idea. There is only Mathematica's > AsymptoticDSolveValue which is just for ODEs.
Well, FriCAS has 'seriesSolve'. For ODEs it should work directly. For PDE you would need some preprocessing. > So I decided to implement it > myself. Thanks to the Sympy community we now have some progress. I have one > implementation over here > <http://nbviewer.jupyter.org/gist/celliern/b38158d04d9dc3d8079dc44e3b747ac8> > by Nicolas CELLIER <https://github.com/celliern> and some ideas over here > <https://cs.stackexchange.com/questions/95886/algorithm-for-using-power-series-to-numerically-solve-a-partial-differential-equ> > > by me and some of SymPy developers. I was wondering if we could join forces > to come of with a general algorithm, then implementionation on diffrent > languages shouldn't be that difficult. I was wondering if you could take a > look at this question > <https://cs.stackexchange.com/questions/95886/algorithm-for-using-power-series-to-numerically-solve-a-partial-differential-equ> > > and help us out. Well, what you write look strange. Normally, truncated series will be only approximation to true solution so it will _not_ satisfy boundary conditions. IOW, solving in say R^n\times R you want initial data, but no boundary conditions. If your equation is appropriate, then Cauchy-Kovalevskaya theorem says that for given initial data you will get unique power series solution in neighbourhood of initial point. After little preprocessing FriCAS 'seriesSolve' should give you this solution. If assumptions of Cauchy-Kovalevskaya theorem are not satisfied, then it is possible that some transformation will give you new system for which Cauchy-Kovalevskaya method works. FriCAS Jet bundle package can help here. -- Waldek Hebisch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
