Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2759

Review

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

S. A. Okunuga1, A. B. Sofoluwe2, J. O. Ehigie1 and M. A. Akanbi3*
1Department of Mathematics, University of Lagos, Akoka, Lagos. 2Department of Computer Sciences, University of Lagos, Akoka, Lagos. 3Department of Mathematics and Applied Mathematics, University of the Western Cape, South Africa.
Email: [email protected]

  •  Accepted: 19 December 2011
  •  Published: 16 January 2012

Abstract

In this paper a direct integration of second-order Ordinary Differential Equations (ODEs) of the form , , , using the Explicit Runge-Kutta-Nyström method with higher derivatives is presented. Various numerical schemes are derived and tested on standard problems. The higher-order explicit Runge-Kutta-Nyström (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.

 

Key words: Runge–Kutta–Nyström method, HERKN method, higher-order derivatives, second order ordinary differential equations.

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