Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

W. Hundsdorfer, A. Mozartova, M. N. Spijker

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.
Original languageEnglish (US)
Pages (from-to)265-286
Number of pages22
JournalJournal of Scientific Computing
Volume50
Issue number2
DOIs
StatePublished - Apr 29 2011
Externally publishedYes

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