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.
Highlights
This paper deals with the numerical integration of the special fourth-order ordinary differential equations (ODEs) of the form y(iV) (x) = f (x, y), (1)
This paper deals with Runge-Kutta type method denoted by RKFD method for directly solving special fourth-order ODEs of the form y(iV)(x) = f(x, y)
We proved that the RKFD method is zero-stable
Summary
This paper deals with the numerical integration of the special fourth-order ordinary differential equations (ODEs) of the form y(iV) (x) = f (x, y) ,. Many authors have proposed several numerical methods for directly approximating the solutions for the higher-order ODEs; for example, Kayode [8] proposed zero-stable predictor-corrector methods for solving fourthorder ordinary differential equations. This paper primarily aims to construct a one-step method of orders four and five to solve special fourth-order ODEs directly; these new methods are self-starting in nature.
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