Third order extended Runge-Kutta Nystrӧm methods for the solution of special second order differential equations

Abstract

Explicit extended Runge-Kutta Nystrӧm type method is constructed for the numerical ( integration of special second order system of differential equations of the form y . Additional parameters are introduced into classical Runge-Kutta Nystrӧm method in such a way that the first derivative of ¢¢ = ( f x y , ) f x y , ) might be required for the integration. Results from numerical experiments reveal the superiority of the new method over several methods in the scientific literature.