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

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 ⩾ (2π/h)2 the method is absolutely stable. Numerical results are presented for Besselʹs, Legendreʹs and general second order differential equations.