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

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.