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 - <p style="text-align: justify;">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.</p>