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.

Sesappa Rai, A.Ananthakrishnaiah, U.2026-02-05Additive pJournal of Computational and Applied Mathematics, 1996, 67, 2, pp. 271-2763770427https://doi.org/10.1016/0377-0427(94)00127-8https://idr.nitk.ac.in/handle/123456789/280581996Differential equationsFinite difference methodNumerical methodsAdditive parametersGeneral second order initial value problemsIntegrationIn 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.