RADAU13 is an implicit 13th order adaptive Runge-Kutta implementation of the RADAU IIA method by Ernst Hairer and Gerhard Wanner. The Fortran code is available from Ernst Hairer’s website
and a detailled description is available in their book
Hairer, Norsett and Wanner (1993): Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition. Springer Series in Comput. Math., vol. 8.
This package does not use f2py, but instead calls the fortran function from a C extension. The solver features dense/continous output, support for implicit problems with a mass matrix, DAEs up to index 3 and multiple error control algorithms. The python interface includes all features except band-width control (for now), but some of the advanced/complex settings are not documented (yet).
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