I would prefer recommendations that don't require the use of proprietary tools (such as Matlab). I know of two ODE solving options for the Python ecosystem:
- PyDSTool (Dopri, Radau, other Runge-Kutta methods, and whatever
scipy.integrate.odehas access to)
- scipy.integrate (
lsodafrom the Fortran library
odepack-- solver decides whether to use a Adams method or a BDF method depending on the stiffness of the problem; dopri5, and dopri853 are also available, along with some solvers for complex ODE systems)
I like Python because I can now write C-speed code, combined with Python flexibility using Python-to-C compilers provided by packages such as Cython. Plus, everything is pretty open-source!
In my early conversations with the developer of PyDSTool, I know he brought up that Radau might be particularly good for non-linear, stiff ODE problems -- and certainly the pure C implementation included with PyDSTool would be much faster than
scipy.integrate's standard ODE solvers. I wasn't really able to understand him well at the time simply due to my lack of mathematical background (I am a math undergrad, recently transferred from engineering). Could you comment on concerns like that -- in particular, what features of my problem do I need to identify in order to figure out which solver is best suited for my system of non-linear ODEs?