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On monotonicity and boundedness properties of linear multistep methods
Author(s):
Willem
Hundsdorfer;
Steven
J.
Ruuth.
Journal:
Math. Comp.
75
(2006),
655-672.
MSC (2000):
Primary 65L06, 65M06, 65M20
Posted:
November 17, 2005
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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:
10.1090/S0025-5718-05-01794-1
PII:
S 0025-5718(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
Posted:
November 17, 2005
Additional Notes:
The work of the second author was partially supported by a grant from NSERC Canada.
Copyright of article:
Copyright
2005,
American Mathematical Society
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