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.

Received: February 19, 2013

AMS Subject Classification: 65205, 65L06, 65D30

Key Words and Phrases: collocation, interpolation, approximate solution, continuous block method, discrete block method, convergent

Download paper from here.