Numerical methods for the simulation of trapped nonlinear Schrödinger systems

• Published in: Applied mathematics and computation Vol. 144; no. 2; pp. 215 - 235
• Main Authors: Pérez-Garcı́a, Vı́ctor M., Liu, Xiao-yan
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 10.12.2003; Elsevier
• Subjects: Exact sciences and technology; Finite difference schemes; Mathematical analysis; Mathematics; Nonlinear Schrödinger equations; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Pseudospectral schemes; Sciences and techniques of general use; Symplectic schemes; Pseudospectral schemes; Symplectic schemes; Nonlinear Schrödinger equations; Finite difference schemes; Solitary wave; Difference scheme; Numerical method; Non linear system; Schrödinger equation; Partial differential equation; Discretization method; Matrix form; Non linear equation; Simulation; Pseudospectral method; Numerical solution; Symplectic method; Numerical simulation; Stationary solution; Finite difference method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/S0096-3003(02)00402-2

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.