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Linearly implicit methods for nonlinear parabolic equations
Author(s):
Georgios
Akrivis;
Michel
Crouzeix.
Journal:
Math. Comp.
73
(2004),
613-635.
MSC (2000):
Primary 65M60, 65M12;
Secondary 65L06
Posted:
June 19, 2003
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Additional information
Abstract:
We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular cases implicit-explicit multistep schemes as well as the combination of implicit Runge-Kutta schemes and extrapolation. An optimal condition for the stability constant is derived under which the schemes are locally stable. We establish optimal order error estimates.
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Additional Information:
Georgios
Akrivis
Affiliation:
Computer Science Department, University of Ioannina, 451 10 Ioannina, Greece
Email:
akrivis@cs.uoi.gr
Michel
Crouzeix
Affiliation:
IRMAR, Université de Rennes I, Campus de Beaulieu, F-35042 Rennes, France
Email:
michel.crouzeix@univ-rennes1.fr
DOI:
10.1090/S0025-5718-03-01573-4
PII:
S 0025-5718(03)01573-4
Keywords:
Nonlinear parabolic equations,
linearly implicit methods,
strong $A(0)$-stability,
implicit-explicit multistep schemes,
polynomial order
Received by editor(s):
May 2, 2001
Received by editor(s) in revised form:
October 2, 2002
Posted:
June 19, 2003
Additional Notes:
The work of the first author was supported in part by the Greek Secretariat for Research and Technology through the PENED Program, no 99ED 275
Copyright of article:
Copyright
2003,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article N. Yu. Bakaev, Linear Discrete Parabolic Problems, North-Holland Mathematical Studies, vol. 203, first, Elsevier, Amsterdam, 2006. (English)
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