A New Formulation for Symmetric Implicit Runge-Kutta-Nystrom Method for the Integration of General Second Order ODEs

Abstract

Symmetric Runge-Kutta –Nystrom Methods are of much current interest due to their efficiency when solving stiff systems and the possibility to use them as basic methods for extrapolation processes.In this paper we derive symmetric stable Implicit Runge-Kutta –Nystrom Method for the Integration of General Second Order ODEs by using the collocation approach.The block hybrid method obtained by the evaluation of the continuous interpolant at different nodes of the polynomial is symmetric and suitable for stiff intial value ODEs problems. We further coverted the uniformly accurate order six block hybrid method to symmetric Implicit Runge-Kutta –Nystrom Method by using the direct method as those invented by Nystrom.The convergence of the method is achieved as shown in the table of results.

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 575 – 582