Nonautonomous stability of linear multistep methods

B R Boutelje, Adrian T Hill

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


A linear scalar nonautonomous initial-value problem (IVP) is governed by a scalar lambda(t) with a nonpositive real part. For a wide class of linear multistep methods, including BDF4-6, it is shown that negative real lambda(t) may be chosen to generate instability in the method when applied to the IVP. However, a uniform-in-time stability result holds when lambda(.) is a Lipschitz function, subject to a related restriction on h. The proof involves the construction of a Lyapunov function based on a convex combination of G-norms.
Original languageEnglish
Pages (from-to)525-542
Number of pages18
JournalIMA Journal of Numerical Analysis
Issue number2
Early online date20 Feb 2009
Publication statusPublished - Apr 2010


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