151. Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations.
- Author
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Hussain, Kasim, Ismail, Fudziah, and Senu, Norazak
- Subjects
- *
RUNGE-Kutta formulas , *ORDINARY differential equations , *STABILITY theory , *NUMERICAL analysis , *ROBUST control , *PROBLEM solving - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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