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On monotonicity and boundedness properties of linear multistep methods


Authors: Willem Hundsdorfer and Steven J. Ruuth
Journal: Math. Comp. 75 (2006), 655-672
MSC (2000): Primary 65L06, 65M06, 65M20
DOI: https://doi.org/10.1090/S0025-5718-05-01794-1
Published electronically: November 17, 2005
MathSciNet review: 2196985
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Abstract: In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also consider contractivity and stability in arbitrary norms.


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Additional Information

Willem Hundsdorfer
Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Email: willem.hundsdorfer@cwi.nl

Steven J. Ruuth
Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 Canada
Email: sruuth@sfu.ca

DOI: https://doi.org/10.1090/S0025-5718-05-01794-1
Keywords: Multistep schemes, monotonicity, boundedness, TVD, TVB, contractivity, stability
Received by editor(s): March 10, 2004
Received by editor(s) in revised form: January 6, 2005
Published electronically: November 17, 2005
Additional Notes: The work of the second author was partially supported by a grant from NSERC Canada.
Article copyright: © Copyright 2005 American Mathematical Society