On a class of multistep methods with strong contractivity properties

AbstractIn this paper we study some contractivity properties of second-derivative linear multistep methods—(SD)LMM—when a test equation of type y′ = λ(t)y is used. Necessary and sufficient conditions for a (SD)LMM to be contractive in some interval of the negative real axis are constructed. A class of A0-contractive (SD)LMMs with any number of k steps, order 2 and depending on k − 1 free parameters, is also presented.Furthermore we prove that this class is A-contractive or A(α)-contractive when a test equation of type y′ = λy is used