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

Abstract

In this paper, we present a block method for the direct solution of third 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 one-step block method is consistent and A -stable, with good region of absolute stability. Experimental results confirmed the superiority of the new scheme over an existing method.

Keywords: consistent, convergent, collocation, hybrid points, independent solution, interpolation, zero stable