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Multiplier and contractivity methods for linear multistep methods

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
5
Identifiers
DOI: 10.1016/0168-9274(89)90026-3
Disciplines
  • Mathematics

Abstract

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.

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