Nonlinear stability of linear multistep methods for stiff delay differential equations in Banach spaces

Abstract

This paper is concerned with the nonlinear stability properties of a class of linear multistep methods when applied to initial value problems of stiff delay differential equations in Banach spaces. For the test problem classes D( α, λ ∗, β) and D( α, λ ∗, δ, β) in Banach spaces, a series of new stability results of the linear multistep methods are obtained.