Development of a New One step Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations

This paper presents the development and implementation of an explicit rational one step method of order four for solving initial value problems of ordinary differential equations. The scheme has been derived through the combination of two interpolants namely, polynomial and rational transcendental form of expo nential and trigonometric functions. The method was used for the solution of four initial values problems in which two of them are nonlinear IVPs. The numerical results showed that the new scheme is consistent with the initial value, robust and efficient.