Runge-Kutta-Nyström methods for general second order ODEs with application to multi-body systems Original Research Article

The numerical integration of non-stiff second order ODE systems View the MathML source by means of Runge-Kutta-Nyström methods is considered. It is assumed that the right-hand side of the system does depend on View the MathML source but a considerable amount of intermediate calculations needed to evaluate View the MathML source only depend on q and t. Such systems often arise in practice, in particular, in multi-body system simulation. We construct three particular Runge-Kutta-Nyström methods for general second order ODEs, two methods of order five, and one of order six. Numerical comparisons are presented, which show that Runge-Kutta-Nyström schemes can be constructed that are more efficient than explicit Runge-Kutta methods when applied to non-stiff multi-body systems.