An Order-seven Implicit Symmetric Scheme Applied to Second Order Initial Value Problems of Differential Equations

Abstract

In this paper, a five-step predictor-corrector method of algebraic order seven is presented for solving second order initial value problems of ordinary differential equations directly without reduction to first order systems. Analysis of the basic properties of the method is considered and found to be consistent, zero-stable and symmetric. Some sample linear and nonlinear problems are solved to demonstrate the applicability of the method. It is observed that the present method approximates the exact solution well when compared with the two existing schemes that solved the same set of problems.

Keywords: zero-stability, convergence, consistent, predictor-corrector, error constant, symmetric