On Extension the Stability Region of Implicit-Explicit Linear Multistep Methods for Ordinary Differential Equation

Abstract Stability properties of implicit explicit (IMEX) of linear multistep methods for ordinary differential equations are analyzed on the basis of stability regions defined by using scalar test equations. This study is closely related to the stability analysis of the standard linear multistep methods for ordinary differential equation. In this paper we give two idea to extend the stability region for the second order IMEX method, also have extended the region IMEX Euler method, the simplest IMEX method of first order, numerical results