A spatial sixth-order alternating direction implicit method for two-dimensional cubic nonlinear Schrödinger equations

DOI10.1016/j.cpc.2014.10.008zbMath1348.35238OpenAlexW2039233082MaRDI QIDQ337710

Sik-Chung Tam, Hai-Wei Sun, Leonard Z. Li

Publication date: 10 November 2016

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

Full work available at URL: https://doi.org/10.1016/j.cpc.2014.10.008

zbMATH Keywords

unconditional stabilityalternating direction implicit methodcubic nonlinear Schrödinger equationcombined compact difference schemesolution patternwave-like motion

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

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• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• A CCD-ADI method for unsteady convection-diffusion equations
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• High-order compact ADI (HOC-ADI) method for solving unsteady 2D Schrödinger equation
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• Split-step orthogonal spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions
• High-order compact exponential finite difference methods for convection-diffusion type problems
• Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• A three-point combined compact difference scheme
• High order ADI method for solving unsteady convection-diffusion problems
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation
• A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator
• A fourth-order compact ADI method for solving two-dimensional unsteady convection--diffusion problems
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Structure of a quantized vortex in boson systems
• A high-order finite difference discretization strategy based on extrapolation for convection diffusion equations
• Dynamic properties of cubic nonlinear Schrödinger equation with varying nonlinear parameter
• Numerical Study of Quantized Vortex Interactions in the Nonlinear Schrödinger Equation on Bounded Domains
• The Dynamics and Interaction of Quantized Vortices in the Ginzburg–Landau–Schrödinger Equation
• Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
• A New Computational Procedure for A.D.I. Methods

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