On Friday, August 3, 2018 at 9:51:44 PM UTC+2, Waldek Hebisch wrote: > > 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.
This awesome. Could you be so kind to pint me to the source code? I want to learn the algorithm. > For PDE you would need some preprocessing. > If you have any ideas for the algorithm please share over here <https://cs.stackexchange.com/questions/95886/algorithm-for-using-power-series-to-numerically-solve-a-partial-differential-equ> > > > 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. disclaimer, I collected most of the pices from other places, so I'm barely the developer. Would you be so kind to let me know which part doesn't make sense? > Normally, truncated series > will be only approximation to true solution so it will _not_ > satisfy boundary conditions. I'm not sure if I understand your point completely, but I mentioned some solutions to the boundary condition incompatibility over here second comment <https://github.com/sympy/sympy/issues/15015#>. I think integral of the square of the error could be used to minimize the error. > IOW, solving in say R^n\times R > you want initial data, but no boundary conditions. I don not understand this, would you please elaborate? > 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. This was also mentioned here in the Sympy mailing list <https://groups.google.com/forum/#!topic/sympy/X3h38SqQBCo>. I'm going to learn more about this. > After little > preprocessing FriCAS 'seriesSolve' should give you this > solution. > Looking forwards to that. > > 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. > No idea what is this. is there a good link I can read more about it? > > -- > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
