Development of a Two-Step Block Numerov Method with Bhaskara Hybrid Points for Second Order Initial Value Problems

Abstract

This study develops a two- step block Numerov method with two Bhaskara hybrid off-grid points for the direct solution of second order initial value problems. A power series polynomial is interpolated and collocated at selected off grid and hybrid points to obtain a continuous scheme, from which a block of discrete schemes is derived and solved simultaneously. The block has orders 5, 5 and 6 and its error constants, consistency, zero stability and convergence are established. Numerical experiments on three test problems with known exact solutions show close agreement between the numerical and exact solutions. The result indicated that the method is an accurate direct solver for second order initial value problems.