Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations

Abstract EN

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.