ALGLIB package implement Runge-Kutta-Cash-Karp adaptive integrator to solve ordinary differential equations. Cash-Karp method uses six function evaluations to calculate 4-th and fifth-order accurate solutions. One of them is used to advance solution, another is used as the error estimate.
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C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
Python version (CPython and IronPython are supported).