Fifth order two-stage explicit Runge-Kutta-Nystrom method for the direct integration of second order ordinary differential equations

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Date

2012

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Journal ISSN

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Publisher

Academic Journals

Abstract

In this paper a direct integration of second-order Ordinary Differential Equations (ODEs) of the form using the Explicit Runge-Kutta-Nystrom method with higher derivatives is presented. Various numerical schemes are derived and tested on standard problems. The higher-order explicit Runge-Kutta-Nystrom (HERKN) method given in this paper is compared with the conventional Explicit Runge Kutta (ERK) schemes. Due to the limitation of ERK schemes in handling stiff problems, the extension to higher order derivative is considered. The results obtained show an improvement on ERK schemes.

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Keywords

Runge-Kutta-Nystrom method, HERKN method, Higher-order derivatives, Second order ordinary differential equations, Ordinary Differential Equations (ODEs)

Citation

Okunuga, S.A et al. (2012). Fifth order two-stage explicit Runge-Kutta-Nystrom method for the direct integration of second order ordinary differential equations. Scientific Research and Essays, 7(2): 134-144