Dormand-Prince

In numerical analysis, Dormand-Prince is a method for solving ordinary differential equations (ODEs). The method is a member of the Runge-Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions. The difference between these solutions is then taken to be the error of the (fourth order) solution. This error estimate is very convenient for adaptive stepsize integration algorithms. Other similar integration methods are Fehlberg (RKF) and Cash-Karp (RKCK). Fehlberg was the inventor of this type of "embedded" error formulas.

Dormand-Prince is currently the default method in MATLAB's ode45 solver (as of version 7.3) and is the default choice for the Simulink's model explorer solver.

An open source implementation of the algorithm called DOPRI5 is also available http://www.unige.ch/~hairer/prog/nonstiff/dopri5.f

References

* Dormand J, Prince P. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, Volume 6, pages 19-26 (1980)