The Taylor method for ODEs has alredy been implemented within the TaylorSeries.jl <https://github.com/JuliaDiff/TaylorSeries.jl> package, although maybe not too user friendly. Check out the Kepler problem <https://github.com/JuliaDiff/TaylorSeries.jl/blob/master/examples/User%20guide.ipynb> example.
El viernes, 26 de febrero de 2016, 9:08:06 (UTC-6), [email protected] escribió: > > Hi Mauro, > > I would like to submit a proposal to work on the ODE.jl package, > for the GSoC. From my undergraduate and master thesis I have > experience with the Taylor method for solving ODEs (ie., based on Taylor > series expansions). This is a variable order, variable step > size method, which uses automatic differentiation > techniques in order to reach high order integration methods (30th, 40th > order) > which enable machine-epsilon precision with very competitive speeds. > I think the Taylor method is important to include in the ODE.jl package, > as it is very versatile and precise. > > Besides the utility of the Taylor method for ODEs integration, a DAEs > solver can > also be implemented using the Taylor models framework. > > I would be very happy to contribute to the ODE.jl package! > > Best regards, > > On Thursday, February 11, 2016 at 7:56:45 AM UTC-6, Mauro wrote: >> >> >> It is desirable to have ode-solvers which are pure Julia. Both to cut >> down on dependencies and to allow easy hacking and development. >> Further, Sundials.jl will not work with generic Julia datatypes (e.g. I >> think Julia sparse matrices are not supported for Jacobians). Thus, >> ODE.jl is to stay and to be improved on. >> >> The currently ongoing work of which I'm aware is: >> https://github.com/JuliaLang/ODE.jl/pull/49 >> https://github.com/JuliaLang/ODE.jl/pull/72 >> >> Needed work is: >> - more solvers >> - a unified code structure/API >> - parallelism(?) >> >> I'll try and update the GSoC description. >> >
