The International Institute for Science, Technology and Education (IISTE)
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 stabl
