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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05
Acknowledgements: The work of A. Mozartova is supported by a grant from the Netherlands Organisation for Scientific Research NWO. The work of W. Hundsdorfer for this publication was partially supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.