A new hybrid block method for the solution of general third order initial value problems of ordinary differential equations

Abstract

In this paper, we develop an order six block method using method of collocation and interpolation of power series approximate solution to give a system of non linear equations which is solved to give a continuous hybrid linear multistep method. The continous hybrid linear multistep method is solved for the independent solutions to give a continous hybrid block method which is then evaluated at some selected grid points to give a discrete block method. The basic properties of the discrete block method was investigated and found to be zero stable, consistent and convergent. The derived scheme was tested on some numerical examples and was found to give better approximation than the existing method. © 2013 Academic Publications, Ltd.