High order stiffly stable parameter dependent nested hybrid linear multistep methods for stiff ODEs

Abstract

In this work, we proposed a High Order Stiffly Stable parameter dependent nested hybrid linear multistep method for stiff initial value problems (IVPs) in ordinary differential equations (ODEs). It forms a super class of the linear multistep methods (LMMs), with properties that embedded the characteristics of LMM and hybrid methods. It is hybrid in nature as a result of the incorporation of one or more off-step points and this is aimed at attaining a better stability properties and higher order than the conventional linear multistep methods (LMMs). The proposed method is A- stable and A(α) –stable for step number k ≤ 6. A numerical example is given to demonstrate the application of the methods.