Year: 2016
Author: Begoña Cano, Adolfo González-Pachón
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 4 : pp. 385–406
Abstract
Numerical stability when integrating plane waves of cubic Schrödinger equation is thoroughly analysed for some explicit exponential methods. We center on the following second-order methods: Strang splitting and Lawson method based on a one-parameter family of 2-stage 2nd-order explicit Runge-Kutta methods. Regions of stability are plotted and numerical results are shown which corroborate the theoretical results. Besides, a technique is suggested to avoid the possible numerical instabilities which do not correspond to continuous ones.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1601-m4541
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 4 : pp. 385–406
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Numerical stability Exponential splitting Lawson methods Projection onto invariant quantities Plane waves
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