A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs

• Main Authors: Fudziah Ismail, Hussain, Kasim, Norazak Senu
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2016
• Online Access: http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf; http://journalarticle.ukm.my/10395/; http://www.ukm.my/jsm/english_journals/vol45num11_2016/contentsVol45num11_2016.html
• Institution: Universiti Kebangsaan Malaysia

In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order RKFD method denoted as RKFD6 method. Zero-stability of the method is proven. Comparisons are made using the existing Runge–Kutta methods after the problems are reduced to a system of first order ordinary differential equations. Numerical results are presented to illustrate the efficiency and competency of the new method.