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Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations

Authors: Eskil Hansen and Tony Stillfjord
Journal: Math. Comp. 82 (2013), 1975-1985
MSC (2010): Primary 65J08, 65M15, 47H06
Published electronically: April 30, 2013
MathSciNet review: 3073188
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Abstract: We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler schemes have the same convergence order, i.e., between one half and one depending on the initial values and the vector fields. Concrete applications include the discretization of diffusion-reaction systems, with fully nonlinear and degenerate diffusion terms. The convergence and efficiency of the IMEX Euler scheme are also illustrated by a set of numerical experiments.

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Additional Information

Eskil Hansen
Affiliation: Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden

Tony Stillfjord
Affiliation: Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden

Keywords: Implicit-explicit Euler scheme, convergence orders, nonlinear evolution equations, dissipative operators
Received by editor(s): June 17, 2011
Received by editor(s) in revised form: January 9, 2012
Published electronically: April 30, 2013
Additional Notes: The work of the first author was supported by the Swedish Research Council under grant 621-2007-6227.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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