Eleventh Order Hybrid Block Method for the Solution of Nonlinear First Order Initial Value Problems

Abstract

In this paper, the development of three-step eleventh order hybrid block method for the solution of nonlinear first order initial value problems using power series approximation is discussed. The interpolation and collocation method was adopted in the development of the continuous linear method. The result was evaluated at selected grid points to give a discrete block which eventually gave simultaneous solutions at both grid and off grid points. The three-step block method is consistent, zero stable and therefore convergent. Experimental results confirmed the superiority of the new scheme over an existing method.