A Runge-Kutta starter for a multistep method for differential-algebraic systems with discontinuous effects (Q1902084)

The authors consider the numerical solution of differential equations, for which multistep methods require frequent restarts (e.g., in the presence of discontinuities). Instead of starting each time with a first- order method and very small stepsizes, they suggest to start with higher- order approximations and larger stepsizes, taking the necessary information from a suitable Runge-Kutta method. For this purpose, they construct a 6-stage Runge-Kutta method of order 4, which provides third- order approximations at equidistant points. Numerical experiments with problems from multibody system dynamics illustrate the efficiency of the new procedure.