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

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.