On the generation of higher order numerical integration methods using lower order Adams-Bashforth and Adams-Moulton methods

Abstract

In this paper, a new explicit numerical integration method is proposed. The proposed method is based on the relationship that m-step Adams-Moulton method is the linear convex, combination of (m - 1)-step Adams-Moulton and m-step Adams-Bashforth methods with a fixed weighting coefficient. By examining the order of accuracy and stability regions, we conclude that the present method is superior to the traditional Adams-Bashforth-Moulton predictor-corrector method. A simple harmonic oscillator problem is used to demonstrate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.