A One-Step Method for the Numerical Integration of the Differential Equation y'' = f(x)y + g(x)

Abstract

1. The numerical integration of ordinary differential equations by the use of Gaussian quadrature methods was introduced into the literature by Hammer and Hollingsworth (1955), for subsequent developments, see Morrison and Stoller (1958), Korganoff (1958), Kuntzmann (1961), Henrici (1962). In this paper we develop a one-step method for the numerical integration of the ordinary differential equation y = f(x)y + g{x), y(o) — .Vo> y(*o) — yo based on the Gauss two-point rule (see Hildebrand, 1956). Theoretical and computational comparison of the new method with other methods is given.