Linearly implicit methods for nonlinear parabolic equations
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- by Georgios Akrivis and Michel Crouzeix PDF
- Math. Comp. 73 (2004), 613-635 Request permission
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.References
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Additional Information
- Georgios Akrivis
- Affiliation: Computer Science Department, University of Ioannina, 451 10 Ioannina, Greece
- MR Author ID: 24080
- 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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 613-635
- MSC (2000): Primary 65M60, 65M12; Secondary 65L06
- DOI: https://doi.org/10.1090/S0025-5718-03-01573-4
- MathSciNet review: 2031397