IJPAM: Volume 109, No. 2 (2016)

NEW EXPLICIT TRIGONOMETRICALLY-FITTED
FOURTH-ORDER AND FIFTH-ORDER
RUNGE-KUTTA-NYSTRÖM METHODS FOR
PERIODIC INITIAL VALUE PROBLEMS

M.A. Demba$^1$, N. Senu$^2$, F. Ismail$^3$
$^1$Department of Mathematics
Universiti Putra Malaysia
43400 UPM Serdang, Selangor, MALAYSIA
$^{2,3}$Department of Mathematics
and Institute for Mathematical Research
Universiti Putra Malaysia
43400 UPM Serdang, Selangor, MALAYSIA


Abstract. In this work, we derive two new Runge-Kutta-Nyström (RKN) methods for solving periodic second order ordinary differential equations. We constructed these methods based on the RKN method of three-stage fourth-order derived by Garcia and RKN method of four-stage fifth-order derived by Hairer. The numerical results show that the efficiency of the new methods is more than the other existing methods.

Received: May 21, 2016

AMS Subject Classification: 65L05, 65L06

Key Words and Phrases: trigonometric fitting, RKN methods, periodic initial value problems

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DOI: 10.12732/ijpam.v109i2.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 207 - 221


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