Algorithm 968

Abstract

In this article, an adaptive Runge-Kutta code, based on the DOPRI5(4) pair for solving initial value problems (IVPs) for differential systems with piecewise smooth solutions (PWS) is presented and the algorithms used in the code are described. The code automatically detects and locates accurately the switching points of the PWS, restarting the integration after each discontinuity. Further, in the case of Filippov systems, algorithms to handle properly sliding mode regimes in an automatic way are included. The code requires the user to provide a description of the IVP and the functions defining the hypersurfaces where the switching points are located, and it returns the discrete approximated solution together with the switching points. Several numerical experiments are presented to illustrate the reliability and efficiency of the code.