On the construction of high order $A(\alpha)$-stable hybrid linear multistep methods for stiff IVPs in ODEs

In this paper, we present a class of $A(\alpha)$-stable hybrid linear multistep methods for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The method considered uses a second derivative like the Enright's second derivative linear multistep methods for stiff IVPs in ODEs.