Multiplier and contractivity methods for linear multistep methods

Abstract

We survey informally some results on the stability of linear multistep and one-leg methods for stiff nonlinear differential equations. The results discussed are of two types: (a) functional-analytic techniques appropriate for studying high-order methods, and their application to global iteration schemes; and (b) Liapunov-like methods for analyzing the effects of variable time steps and coefficients, and for deriving low-order methods which are insensitive to such variability. © 1989.