A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs

摘要

In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK)methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered.The TDTSRK methods are a special case of multiderivative Runge-Kutta methods proposed by Kastlunger andWanner (1972). Themethods considered herein incorporate only the first and second derivatives terms of ODEs. These methods possess large interval of stability when compared with other existing methods in the literature.The experiments have been performed on standard problems, and comparisons were made with some standard explicit Runge-Kutta methods in the literature.