An Order Four Block Method with Three Generalized Off Step Points for Solving First Order Ordinary Differential Equations

Abstract

This paper presents a single-step block method with three generalized off-step points for solving first order ordinary differential equations. The approach employed in developing this new method is interpolating the approximated power series of order four at xn as well as at all off-step points and collocating the derivative of the power series at xn+1. The developed method is zero-stable, consistent, convergent and of order four. The new method has better accuracy than the existing methods when solving first order ordinary differential equations.