# IJPAM: Volume 109, No. 3 (2016)

**NEW EXPLICIT TRIGONOMETRICALLY-FITTED**

FOURTH-ORDER AND FIFTH-ORDER

RUNGE-KUTTA-NYSTRÖM METHODS FOR

PERIODIC INITIAL VALUE PROBLEMS

FOURTH-ORDER AND FIFTH-ORDER

RUNGE-KUTTA-NYSTRÖM METHODS FOR

PERIODIC INITIAL VALUE PROBLEMS

M.A. Demba, N. Senu, F. Ismail

Department of Mathematics

Universiti Putra Malaysia

43400 UPM Serdang, Selangor, MALAYSIA

Department of Mathematics

Institute for Mathematical Research

Universiti Putra Malaysia

43400 UPM Serdang, Selangor, MALAYSIA

Department of Mathematics

Universiti Putra Malaysia

43400 UPM Serdang, Selangor, MALAYSIA

Department of Mathematics

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 22, 2016

**Revised:**July 5, 2016

**Published: **October 1, 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.v109i3.6**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2016

**Volume:**109

**Issue:**3

**Pages:**557 - 571

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**This work is licensed under the Creative Commons Attribution International License (CC BY).**