Implicit–explicit multistep methods for nonlinear parabolic equations

Akrivis, Georgios

doi:10.1090/S0025-5718-2012-02628-7

Implicit–explicit multistep methods for nonlinear parabolic equations
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by Georgios Akrivis;

Math. Comp. 82 (2013), 45-68

DOI: https://doi.org/10.1090/S0025-5718-2012-02628-7

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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