Refinements of the Egyptian Fraction Finite Difference Scheme for First and Second Order Initial Value Problems.

Abstract

In this paper, new methods, which are akin to both Runge-Kutta methods and Quasi-Runge- Kutta methods, through a refinement process by Taylor’s series expansion of the error term of the existing Egyptian fraction method, were derived. They are less cumbersome than the Hybrid methods while maintaining high accuracy of the numerical results. The methods are used to solve both first and second order differential equations with initial conditions and the results obtained are very favourable because they produced lower absolute error when compared with the existing similar methods.