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Linearly implicit methods for nonlinear parabolic equations

Authors: Georgios Akrivis and Michel Crouzeix
Journal: Math. Comp. 73 (2004), 613-635
MSC (2000): Primary 65M60, 65M12; Secondary 65L06
Published electronically: June 19, 2003
MathSciNet review: 2031397
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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

Michel Crouzeix
Affiliation: IRMAR, Université de Rennes I, Campus de Beaulieu, F-35042 Rennes, France

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
Published electronically: 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
Article copyright: © Copyright 2003 American Mathematical Society

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