Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation

Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation

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

Author Details

Begoña Cano

Adolfo González-Pachón