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Mathematics of Computation

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Stability properties of implicit–explicit multistep methods for a class of nonlinear parabolic equations

Author: Georgios Akrivis
Journal: Math. Comp. 85 (2016), 2217-2229
MSC (2010): Primary 65M12, 65M60; Secondary 65L06.
Published electronically: December 16, 2015
MathSciNet review: 3511280
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Abstract: We consider the discretization of a special class of nonlinear parabolic equations, including the complex Ginzburg–Landau equation, by implicit–explicit multistep methods and establish stability under a best possible linear stability condition.

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Additional Information

Georgios Akrivis
Affiliation: Department of Computer Science and Engineering, University of Ioannina, 451$\,$10 Ioannina, Greece
MR Author ID: 24080

Keywords: Nonlinear parabolic equations, complex Ginzburg–Landau equation, implicit–explicit multistep methods, BDF methods, strong $A$$(0)-$stability, $A(\vartheta )-$stability, stability condition
Received by editor(s): April 22, 2014
Received by editor(s) in revised form: February 25, 2015, and March 30, 2015
Published electronically: December 16, 2015
Additional Notes: This work was supported in part by GSRT-ESET “Excellence” grant 1456.
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.