Additive parameters methods for the numerical integration of y? = f (t, y, y?)

Abstract

In this paper numerical methods for the initial value problems of general second order differential equations are derived. The methods depend upon the parameters p and q which are the new additional values of the coefficients of y? and y in the given differential equation. Here, we report a new two step fourth order method. As p tends to zero and q ? (2?/h)2 the method is absolutely stable. Numerical results are presented for Bessel's, Legendre's and general second order differential equations.