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Mathematical Problems in Engineering - Volume 2015 2015, Article ID 893763, 11 pages -

Research Article

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia UPM, 43400 Serdang, Selangor, Malaysia

Department of Mathematics, College of Science, Al-Mustansiriya University, Baghdad, Iraq

Institute for Mathematical Research, Universiti Putra Malaysia UPM, 43400 Serdang, Selangor, Malaysia

Received 25 May 2015; Revised 14 July 2015; Accepted 21 July 2015

Academic Editor: Yan-Jun Liu

Copyright © 2015 Kasim Hussain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Runge-Kutta type method for directly solving special fourth-order ordinary differential equations ODEs which is denoted by RKFD method is constructed. The order conditions of RKFD method up to order five are derived; based on the order conditions, three-stage fourth- and fifth-order Runge-Kutta type methods are constructed. Zero-stability of the RKFD method is proven. Numerical results obtained are compared with the existing Runge-Kutta methods in the scientific literature after reducing the problems into a system of first-order ODEs and solving them. Numerical results are presented to illustrate the robustness and competency of the new methods in terms of accuracy and number of function evaluations.





Autor: Kasim Hussain, Fudziah Ismail, and Norazak Senu

Fuente: https://www.hindawi.com/



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