An Explicit Time-Difference Scheme with an Adams–Bashforth Predictor and a Trapezoidal Corrector

Abstract

A new predictor-corrector time-difference scheme that employs a second-order Adams?Bashforth scheme for the predictor and a trapezoidal scheme for the corrector is introduced. The von Neumann stability properties of the proposed Adams?Bashforth trapezoidal scheme are determined for the oscillation and friction equations. Effectiveness of the scheme is demonstrated through a number of time integrations using finite-difference numerical models of varying complexities in one and two spatial dimensions. The proposed scheme has useful implications for the fully implicit schemes currently employed in some semi-Lagrangian models of the atmosphere.