Symmetric Two-Step Runge-Kutta Collocation Methods For Stiff Systems Of Ordinary Differential Equations

Abstract

Symmetric two-step Runge-Kutta collocation methods have been derived for solution of stiff and oscillatory differential equations. The methods are of orders six and eight with five and seven stages respectively and hence substantial improvements in efficiency and flexibility are achieved when using them. They are shown to be A-stable, self-starting, convergent and cope effectively with stable systems of initial value problems with large Lipschitz constants. These methods as compared, for example, with some other recently derived methods of the same order, provide approximations of high accuracy to solutions of systems of initial value problems in ordinary differential equations over the entire interval of integration. The analytic discussion is confirmed by numerical examples