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

• Main Authors: Ismail, Fudziah, Hussain, Kasim, Senu, Norazak
• Format: Article
• Language: English
• Published: Universiti Kebangsaan Malaysia 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/54939/1/A%20sixth-order%20RKFD%20method%20with%20four-stage%20for%20directly%20solving%20special%20fourth-order%20.pdf; http://psasir.upm.edu.my/id/eprint/54939/
• Institution: Universiti Putra 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.