Some implementation aspects of the general linear methods withinherent Runge-Kutta stability

Abstract

In this paper we try to put dierent practical aspects of the general linear methods discussed in the papers (1,6,7) under one algorithm to show more details of its implementation. With a proposed initial step size strategy this algorithm shows a better performance in some problems. To illustrate the eciency of the method we consider some standard test problems and report more useful details of step size and order changes, and number of rejected and accepted steps along with relative global errors.