A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs

summary:In this paper, a class of A($\alpha $)-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k\le 3$ and stiffly stable for $k=4, 5$ and $6$. Some numerical results are reported to illustrate the method