On May 5, 7:04 am, Thierry Dumont <tdum...@math.univ-lyon1.fr> wrote:
> If it is possible, I propose (me) to make a package of ODE/DAE > intergrators: ther is a lot of methods which would be nice in Sage like > Implicit R-K methods, Symplectic methods and so on... I naively volunteer to help on setting a package with updated ODE/DAE solvers. First of all I should disclaim that I just started with Sage. I can do my tricks with Python, but I have a very distant view of Cython. I do have some experience with Fortran90, and C. I'm coming from finite element codes. I just have a rough idea about ODE/DAE. Further I will be using this things anyway for my PhD which I just started. IDA (also used by Mathematica) is the latest code from the Lawrence Livermore family of solvers [https://computation.llnl.gov/casc/sundials/ main.html]. If Sage wants a 'viable alternative to Mathematica' I think it is worth to have the *very same* solver. The interface Python-Sundials [http://code.google.com/p/python- sundials/] has a Cython wrapper for CVODE, IDA, KINSOL. I actually compiled Sundials and gave it a try on the CVODE demo. It worked nice on my linux box after the developer fixed a little bug. This interface seem really fresh and we could learn and improve from there. PySUNDIALS [http://pysundials.sourceforge.net/] seems a bit inactive. I recall reading somewhere it uses Swig instead of Cython. >From what I saw I think the SUNDIALS codes and RADAU should be able to handle a wide variety of stiff ODE/DAEs lurking around. Even you say that Sage ODEs are slow, they still solve non-stiff problems. Radau solves explicit ant implicit ODEs. It can also handle a mass matrix on the LHS, therefore a DAE configuration. I also had a look on the mixed offering of solvers in Scilab, Octave, R and Scipy. Octave an R have a dozen of solvers, including RADAU and DASPK. Scipy offers a Dopri5 which matches well with the Matlab ode45. What are the equivalents or original source for Matlab ode15s, ode23t? Petzold herself et al. point again into DASSL, RADAU5 and SUNDIALS for solving DAE problems http://www.scholarpedia.org/article/Differential-algebraic_equations Ouch, It says also that RADAU5 only handle constant Mass matrix... That is not good for me. Currently my problem is a DAE with state dependent mass matrix. Later it could become time dependent. Actually I aiming at a much larger system of DAEs and I believe IDA will do the job for me. Soon I will also be dealing with stiff ODE systems. I will need some RADAU here. I would be very happy to do all my symbolic calculations, stability analysis and numerical time integration within Sage, within Python. I am willing to write code, but I will need inputs from people out there. Looking forward for further ideas and directions. Regards, -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
