A 5-STEP BLOCK METHOD FOR SPECIAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Various schemes exist to solve the initial/boundary value problems of the ordinary differential equationy00 = f (x,y).Parts of the inadequacies of conventional linear multistep procedures for direct solution of this class of problem is the requirement of a starting value and this paper addressed that. Five specific schemes of orders (6,6,6,6,6)T have been derived and presented in a way to avoid computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations. Furthermore, a stability analysis of the 5-step block method and efficiency of the method is tested on problems whose solutions are, oscillatory or nearly periodic, stiff and non-linear ivp and bvp ODES