Continuous block method for the solution of second order initial value problems of ordinary differential equation

Abstract

We proposed a continuous blocks method for the solution of second order initial value problems with constant step size in this paper. The method was developed by interpolation and collocation of power series approximate solution to generate a continuous linear multistep method; this is evaluated for the independent solution to give a continuous block method which is evaluated at selected grid point to give discrete block method. The basic properties of the method were investigated and was found to be zero stable, consistent and convergent. The efficiency of the method was tested on some numerical examples and found to give better approximation than the existing methods. © 2013 Academic Publications, Ltd.