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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Implicit-explicit multistep methods for nonlinear parabolic equations


Author: Georgios Akrivis
Journal: Math. Comp. 82 (2013), 45-68
MSC (2010): Primary 65M12, 65M60; Secondary 65L06
Published electronically: July 10, 2012
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Abstract: Implicit-explicit multistep methods for nonlinear parabolic equations were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed to be time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by allowing part of it to be time-dependent or nonself-adjoint. We establish optimal order a priori error estimates.


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Additional Information

Georgios Akrivis
Affiliation: Computer Science Department, University of Ioannina, 45110 Ioannina, Greece
Email: akrivis@cs.uoi.gr

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02628-7
PII: S 0025-5718(2012)02628-7
Keywords: Nonlinear parabolic equations, implicit–explicit multistep methods, BDF methods, strong $A(0)$-stability, $A(𝜗)$-stability, $G$-stability
Received by editor(s): April 15, 2011
Received by editor(s) in revised form: September 12, 2011
Published electronically: July 10, 2012
Additional Notes: This work was supported in part by University of Cyprus grant no. 8037P-3/311-21028.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.