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Volume 34, Issue 4
Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation

Begoña Cano & Adolfo González-Pachón

DOI: 10.4208/jcm.1601-m4541

J. Comp. Math., 34 (2016), pp. 385-406.

Published online: 2016-08

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  • 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.

  • Keywords

Numerical stability, Exponential splitting Lawson methods, Projection onto invariant quantities, Plane waves Schrödinger equation.

  • AMS Subject Headings

65M12, 65M15, 65M99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bego@mac.uva.es (Begoña Cano)

adolfogp@mac.uva.es (Adolfo González-Pachón)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-385, author = {Cano , Begoña and González-Pachón , Adolfo}, title = {Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m4541}, url = {http://global-sci.org/intro/article_detail/jcm/9802.html} }
TY - JOUR T1 - Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation AU - Cano , Begoña AU - González-Pachón , Adolfo JO - Journal of Computational Mathematics VL - 4 SP - 385 EP - 406 PY - 2016 DA - 2016/08 SN - 34 DO - http://doi.org/10.4208/jcm.1601-m4541 UR - https://global-sci.org/intro/article_detail/jcm/9802.html KW - Numerical stability, Exponential splitting Lawson methods, Projection onto invariant quantities, Plane waves KW - Schrödinger equation. AB -

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.

Cano , Begoña and González-Pachón , Adolfo. (2016). Plane Waves Numerical Stability of Some Explicit Exponential Methods for Cubic Schrödinger Equation. Journal of Computational Mathematics. 34 (4). 385-406. doi:10.4208/jcm.1601-m4541
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