On the Stability of a High Order Stiffly Stable Parameter Dependent Nested Hybrid Linear Multistep Methods for Stiff ODEs

Abstract

This paper is on the stability of a high order stiffly stable parameter dependent nested hybrid multistep method for the numerical integration of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The method incorporates one or more off-step points for better stability properties. The stability properties of the methods were investigated and the intervals of absolute stability of the methods with step number $k \leq 6$ are presented using the boundary locus techniques. The method is $A$-stable and $A(\alpha)$-stable which makes the methods more suitable for stiff initial value problems.