@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} }