There are many excellent programs available for solving differential equations and computing bifurcations of vector fields. However, each has its own format for specifying the vector field that defines the differential equation. VFGEN lets you define your vector field once (using XML), and export the vector field in several formats. VFGEN uses a C++ symbolic algebra library (GiNaC) to generate Jacobians and higher derivatives automatically.
An article about VFGEN was published in the Journal of Numerical Analysis, Industrial and Applied Mathematics, Volume 3(1-2).
Here, grouped roughly by category, are the output formats available:
ODE solver libraries | CVODE (C), GNU Scientific Library (C), ODEPACK solvers LSODA, LSODAR and LSODE (Fortran 77), MATLAB, Octave, PyGSL (Python), RADAU5 (Fortran 77), Scilab, SciPy (Python) |
Bifurcation analysis | AUTO, DDE-BIFTOOL, DSTool, MATCONT, PDDE-CONT, PyDSTool, XPP |
Delay equations | DDE23 (MATLAB), DDE-BIFTOOL (MATLAB), DDE_SOLVER (Fortran 90), Delay2ODE, PDDE-CONT (C++), XPP |
Dynamical systems programs | DSTool, MATCONT (MATLAB), PyDSTool (Python), XPP |
Other | ADOL-C, Delay2ODE, EVF (variational equations), Javascript, LaTeX, Taylor |