Three Step Continuous Hybrid Block Method for the Solution of y’ = f(x,y)

Abstract

In this paper, we present a block method for the direct solution of first order initial value problems of ordinary differential equations. Collocation and interpolation approach was adopted to generate a continuous linear multistep method which was then solved for the independent solution to give a continuous block method. We evaluated the result 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 zero stable, consistent and convergent. Numerical experiments on some selected problems compared with the exact solution proved the efficiency and accuracy of the derived method.