The Direct Two-Point Block One-Step Method Which is efficient and Suitable for Solving Second-Order Differential Equation

Abstract

Abstract: A direct two-point block one-step method for solving general second-order ordinary differential equations (ODEs) directly is presented in this paper. The one-step block method will solve the second-order ODEs without reducing to first-order equations. The direct solutions of the general second-order ODEs will be calculated at two points simultaneously using variable step size.Two point four step direct implicit block method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The method will estimate the solutions of Initial Value Problems (IVPs) at two points simultaneously by using four backward steps. The method developed is suitable for the numerical integration of non stiff and mildly stiff differential systems. Numerical results are given to compare the efficiency of the developed method to the existence block method.