A three–step discretization scheme for direct numerical solution of second-order ordinary differential equations

Abstract

In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that the method is consistent, zero-stable and convergent. The computer implementation of the method with two sample problems shows that the method is quite suitable for direct solution of second-order differential equations without reformulation as first-order systems.