Numerical methods for the simulation of trapped nonlinear Schrödinger systems. (English) Zbl 1024.65084

Summary: 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.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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