Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation

DOI10.1016/j.cpc.2012.01.006zbMath1277.65073OpenAlexW1987868570MaRDI QIDQ1948867

Yiqiang Xu, Lu-Ming Zhang

Publication date: 25 April 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2012.01.006

zbMATH Keywords

cubic nonlinear Schrödinger equationalternating direction implicitextrapolation techniquehigh-order compact

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55)

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Cites Work

• A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation
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• A variable-step Numerov method for the numerical solution of the Schrödinger equation
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• ADI method -- domain decomposition
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• Structure of a quantized vortex in boson systems
• A generalization of Numerov's method for the numerical solution of the Schrödinger equation in two dimensions

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