Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

A. Mozartova, I. Savostianov, W. Hundsdorfer

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© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
Original languageEnglish (US)
Pages (from-to)159-172
Number of pages14
JournalJournal of Computational and Applied Mathematics
StatePublished - May 2015
Externally publishedYes

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