Numerical methods for the simulation of trapped nonlinear Schrödinger systems

摘要

We propose, analyze and compare the efficiency and accuracy of different numerical schemes for the solution of the nonlinear Schrödinger equation with a trapping potential. In particular we study schemes of finite difference, pseudospectral and spectral types for the space discretization together with explicit symplectic, multistep, split-step and standard variable-step integrators to solve the time evolution. All of these schemes are evaluated comparatively and some recommendations based on their accuracy and computational efficiency are made.