An L-stable extended two-step method for the integration of ordinary differential equations

Abstract

A class of linear multistep methods (LMMs) for the numerical solution of first-order differential and stiff differential equations are considered. The accuracy and stability properties of these methods are investigated. By judicious choice of the coefficients in these formulae a method is derived which is the new method which is shown to be L-stable and so is appropriate for the solution of certain ordinary differential and stiff differential equations. Numerical results are presented for several test problems. (c) 2006 Elsevier Inc. All rights reserved.