2015/07/02 by Christophe Besse, C. Besse, Guillaume Dujardin +6 · 4 citations
Mathematics · Engineering · #Numerical methods for differential equations #Computational Fluid Dynamics and Aerodynamics #Fractional Differential Equations Solutions
paper · doi:10.1137/15m1029047
This article deals with the numerical integration in time of nonlinear Schrödinger equations. The main application is the numerical simulation of rotating Bose--Einstein condensates. The authors perform a change of unknown so that the rotation term disappears and they obtain as a result a nonautonomous nonlinear Schrödinger equation. They consider exponential integrators such as exponential Runge--Kutta methods and Lawson methods. They provide an analysis of the order of convergence and some preservation properties of these methods in a simplified setting and they supplement their results with numerical experiments with realistic physical parameters. Moreover, they compare these methods with the classical split-step methods applied to the same problem.