A Fourth Algebraic Order Explicit TrigonometricallyFitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs

F  A  Fawzi; N  Senu; F  Ismail  and Z  A  Majid

doi:10.17485/ijst/2016/v9i47/97774

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A Fourth Algebraic Order Explicit TrigonometricallyFitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2016/v9i47/97774

Year: 2016, Volume: 9, Issue: 48, Pages: 1-7

Original Article

A Fourth Algebraic Order Explicit TrigonometricallyFitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs

F. A. Fawzi^1*, N. Senu² , F. Ismail² and Z. A. Majid²

¹ Department of Mathematics, Faculty of Computer Science and Mathematics, Tikrit University, Iraq; [email protected]
² Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang - 43400, Selangor, Malaysia
*Author for correspondence
Fawzi
Department of Mathematics
Email:[email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This study has constructed an explicit Trigonometrically-Fitted Modified Runge-Kutta (TFMRK) method for solving firstorder differential equations with periodic solutions. The newly developed method was made according to the method of Runge-Kutta Dorm and to fourth algebraic order. Numerical results for the new method were compared with the existing method, showing the potential of the new method over other existing methods.
Keywords: Runge-Kutta Methods, Trigonometrically-Fitting and Periodic Solutions