Rajeev a écrit :
Ok, but... this is a bit sad, but we do not have the best methods for integrating odes. This would be nice to have (in scipy ?) the most modern methods, and this would not be very difficult to implement them, since these method share a rather common interface with odepack (Gear's method). Real problems are stiff, that is to say (roughly speaking!) that in dU/dt=F(U), the jacobian of F has eigenvalues whose real part are distributed in a large negative interval (say... (-10^7, -1) for the classical example of the Oregonator).Hi, sage has gsl as one of the included packages, which is very good for numerical solution of differential equations. have a look at examples on the wikipage - http://wiki.sagemath.org/interact/diffeq 'Vector Field with Runga-Kutta-Fehlberg' by Schilly is one of my favorites. i hope it will help. Best wishes, Rajeev
Having a rather long experience in ODE solving, my conclusion is that the most universal methods are those of the Radau family (described in the book of Hairer and Wanner "Solving ordinary differential equations" (part 2). These methods are the most robust of all, but they are also the fastest ones, for difficult problems.
I wonder whether this would be interesting to have symplectic integrators, for the integration of Hamiltonian systems.
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