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Zbl 1024.65084
Pérez-García, Víctor M.; Liu, Xiaoyan
Numerical methods for the simulation of trapped nonlinear Schrödinger systems. (English)
[J] Appl. Math. Comput. 144, No.2-3, 215-235 (2003). ISSN 0096-3003

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.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35Q55 NLS-like (nonlinear Schroedinger) equations
65P10 Hamiltonian systems including symplectic integrators
37M15 Symplectic integrators
65M70 Spectral, collocation and related methods (IVP of PDE)

Keywords: pseudospectral schemes; nonlinear Schrödinger equations; finite difference schemes; symplectic schemes; comparison of methods; numerical examples; Hamiltonian systems

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Zentralblatt MATH Berlin [Germany]