A Family of Stiffly Stable Linear Multistep Methods for Stiff and Highly Oscillatory Ordinary Differential Equations

Abstract

This paper suggests a family of stiffly stable linear $k$-step methods with order $k$, for arbitrary $k$. Their stability regions are larger than those of the Gear method. Preliminary numerical test shows that these methods are efficient for stiff systems of ordinary differential equations with characteristic values near the imaginary axis.