Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems

Authors

Mohammed Salih, Department of Computer Sciences, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq.Follow
Fudziah Ismail, Department of Mathematics, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, MalaysiaFollow
Norazak Senu, Department of Mathematics, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, MalaysiaFollow

Abstract

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

Keywords

Amplification fitted, Ordinary differential equations, Oscillatory problems, Phase fitted, Runge-Kutta-Fehlberg method.

Article Type

Special Issue Article

Creative Commons License

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

How to Cite this Article

Salih, Mohammed; Ismail, Fudziah; and Senu, Norazak (2020) "Phase Fitted And Amplification Fitted Of Runge-Kutta-Fehlberg Method Of Order 4(5) For Solving Oscillatory Problems," Baghdad Science Journal: Vol. 17: Iss. 2, Article 29.
DOI: https://doi.org/10.21123/bsj.2020.17.2(SI).0689