Monotonicity-preserving linear multistep methods


Willem Hundsdorfer
Steven J. Ruuth
Raymond J. Spiteri

Author Addresses: 

Willem Hundsdorfer (
P.O. Box 94079,
1090 GB Amsterdam, The Netherlands

Steven J. Ruuth (
Department of Mathematics,
Simon Fraser University,
Burnaby, British Columbia,
V5A 1S6 Canada

Raymond J. Spiteri (
Faculty of Computer Science
Dalhousie University
6050 University Ave.
PO Box 15000
Halifax, Nova Scotia, Canada
B3H 4R2


In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total-variation-bounded (TVB) property. In the analysis the multistep methods are considered in combination with suitable starting procedures. This allows for monotonicity statements for classes of methods which are important and often used in practice but which were thus far not covered by theoretical results.

Tech Report Number: 
Report Date: 
April 23, 2002
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