(Apologies for reviving this old thread, but since I saw a couple of mentions of ODE integration via Taylor's method in the mailing list archive, I thought that some people might be interested)
We just released the latest version of our Taylor integrator heyoka.py: https://github.com/bluescarni/heyoka.py heyoka.py is an implementation of Taylor's method for the numerical integration of systems of ODEs based on automatic differentiation and just-in-time compilation via LLVM. Current features include: - support for both double-precision and extended-precision floating-point types, - the ability to maintain machine precision accuracy over tens of billions of timesteps, - high-precision zero-cost dense output, - fast and accurate event detection, - excellent performance, - batch mode integration to harness the power of modern SIMD instruction sets. heyoka.py needs to represent the ODEs symbolically in order to apply the automatic differentiation rules necessary for an efficient implementation of Taylor's method. For this purpose, heyoka.py uses its own expression system, but in recent versions we added the ability to convert heyoka.py's symbolic expressions to/from SymPy. Here's a simple example of interoperability between heyoka.py and SymPy: https://bluescarni.github.io/heyoka.py/notebooks/sympy_interop.html It should not be difficult in principle to implement similar basic interoperability with Sage's expression system. More tutorials and examples are available here: https://bluescarni.github.io/heyoka.py/tutorials.html https://bluescarni.github.io/heyoka.py/examples.html Thanks and kind regards, Francesco. On Mon, 29 Apr 2019 at 12:12, mmarco <mma...@unizar.es> wrote: > You might be interested in taking a look at tides [1]. It is a library for > integration of ODE's in high precission using precisely automatic > differentiation and Taylor arithmetic. It doesn't use interval arithemtic > (so, no certified computation), but maybe some ideas could be useful. > The way it works is by translating the function that defines your ODE to > c-code and then compiling it. > > There is a tides optional package for sage, and an interface to it. > > > > > [1] https://iuma.unizar.es/es/investigacion/software/TIDES > > El viernes, 19 de abril de 2019, 14:48:09 (UTC+2), Nisoli Isaia escribió: >> >> Dear all, >> I was planning in doing a Cython implementation of Forward automatic >> differentiation and >> Taylor arithmetics as in >> https://press.princeton.edu/titles/9488.html >> to use to implement a library for Sage with rigorous quadrature and >> integration of ODE. >> >> I'm trying to understand which parent class could be the best for these >> objects for them >> to be compatible with Sage coercion model. >> >> What is the usual procedure, I read through >> >> http://doc.sagemath.org/html/en/reference/structure/sage/structure/element.html >> but I'm still confused. >> >> Best wishes >> Isaia >> > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAHExjCvSLtAbMW1KwhsF63ORvJXH55bTb2WkGWXp-OYV3%2BLyVQ%40mail.gmail.com.
