A new fifth order explicit runge-kutta method with four stages for solving initial value problems in ODSs

Abstract

In this paper we present a new four-stage fifth-order explicit method of Runge-Kutta type. The new method is based on a composite derivative strategy and stability and error analyses confirm that the method is stable of fifth order. Two examples are given which illustrate the effectiveness of the method compared to the RK-Nystrom six-stage fifth order method.

Keywords:

• Composite Derivative
• Efficient
• RK-Nystrom 5(6) Method

C.R. Categories:

• G.1.7

^∗Universiti Teknologi. Malaysia, Johor Bahru, Malaysia.

^†Nottingham Trent University, Nottingham U.K.

^∗Universiti Teknologi. Malaysia, Johor Bahru, Malaysia.

^†Nottingham Trent University, Nottingham U.K.

Notes

^∗Universiti Teknologi. Malaysia, Johor Bahru, Malaysia.

^†Nottingham Trent University, Nottingham U.K.