Pérez García, Victor M.. 

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.