Year: 2018
Author: Yaolin Jiang, Zhen Miao
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 542–562
Abstract
A quasi-Newton waveform relaxation (WR) algorithm for semi-linear reaction-diffusion equations is presented at first in this paper. Using the idea of energy estimate, a general proof method for convergence of the continuous case and the discrete case of quasi-Newton WR is given, which appears to be the superlinear rate. The semi-linear wave equation and semi-linear coupled equations can similarly be solved by quasi-Newton WR algorithm and be proved as convergent with the energy inequalities. Finally several parallel numerical experiments are implemented to confirm the effectiveness of the above theories.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1702-m2016-0700
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 542–562
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Waveform relaxation quasi-Newton Energy method Superlinear Parallelism.