A MATRIX SYSTEM FOR COMPUTING THE COEFFICIENTS OF THE ADAMS BASHFORTH-MOULTON PREDICTOR-CORRECTOR FORMULAE

Abstract

This paper seeks to show that the kth order Adams Bashforth and Adams Moultons methods are derivable from simple systems of linear equations. The paper uses the often used method of Taylor series expansion to derive matrix systems that can be solved to give the coefficients of the Adams Bashforth and Adams Moultons predictor-corrector formulae used in the solution of first order ordinary differential equations. The contribution in this paper is meant to reduce the work needed during the derivation of the predictor-corrector formulae. A MATLAB m-file is also include for MATLAB implementation of the method. An illustrative example is given to prove the simplicity of the contribution.