Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants

摘要

An automatic technique for solving discontinuous initial-value problems is developed and justified. The technique is based on the use of local interpolants such as those that have been developed for use with Runge-Kutta formula pairs. Numerical examples are presented to illustrate the significant improvement in efficiency and reliability that results when this technique is used with standard methods.