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Physical problems can be translated into mathematical equations, such as differential equations, which emerge almost in every branch of knowledge. Most times, these special equations do not have solutions in closed form, where the only information concerning the solution is that it is known to exist and to be unique. In this study, we consider the general second-order ordinary differential equation of the form y(x) = f(x, y, y), y(0) = y0, y (0) = δ0, (1) where f is a continuous function which arises frequently in physical problems.

A FAMILY OF HIGH-ORDER MULTIPLE FINITE DIFFERENCE METHODS FOR THE DIRECT SOLUTION OF THE GENERAL SECOND-ORDER INITIAL VALUE PROBLEM