Runge-Kutta Starters for Multistep Methods

Abstract

Runge-Kutta-like formulas which enable a multmtep method to start or restart at a high order after lust one Runge-Kutta (RK) step are presented. These formulas greatly improve the efficiency of mnltistep methods in a situation m which they were previously out performed by RK methodsi e., m which there are problems with frequent dlscontinmties or sudden large increases in derivatives, all of which cause an automatic program to reduce order and step size suddenly. © 1980, ACM. All rights reserved.