ORTHOGONAL-BASED HYBRID BLOCK METHOD FOR SOLVING GENERAL SECOND ORDER INITIAL VALUE PROBLEMS

Abstract

The direct integration of general second order initial value problems is considered in this paper.  We employ a new class of orthogonal polynomials constructed as basis function to develop One Step Hybrid Block Method (OSHBM) adopting collocation technique.  We present the recursive formula of the class of polynomials constructed and give analysis of the basic properties of OSHBM as findings show that the method is accurate and convergent.