A new high-order compact ADI finite difference scheme for solving 3D nonlinear Schrödinger equation

DOI10.1186/s13662-018-1700-1zbMath1455.65128OpenAlexW2888109891MaRDI QIDQ1713527

Rena Eskar, Pengzhan Huang, Xinlong Feng

Publication date: 25 January 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1700-1

zbMATH Keywords

stabilityconservation lawhigh-order scheme3D Schrödinger equationcompact ADI finite difference method

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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• A spatial sixth-order alternating direction implicit method for two-dimensional cubic nonlinear Schrödinger equations
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• The study of a fourth-order multistep ADI method applied to nonlinear delay reaction-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
• The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
• Fourth-order compact solution of the nonlinear Klein-Gordon equation
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• High-order finite difference methods for a second order dual-phase-lagging models of microscale heat transfer
• Spectral-like resolution compact ADI finite difference method for the multi-dimensional Schrödinger equations
• Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation
• Analysis and application of a compact multistep ADI solver for a class of nonlinear viscous wave equations
• High-order ADI finite difference schemes for parabolic equations in the combination technique with application in finance
• A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Numerical Solution of System of N–Coupled NonlinearSchrödinger Equations via Two Variants of the MeshlessLocal Petrov–Galerkin (MLPG) Method
• Convergence of compact ADI method for solving linear Schrödinger equations
• Numerical simulation of singular solutions to the two-dimensional cubic schrödinger equation
• Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method
• Finite difference discretization of the cubic Schrödinger equation
• On the Construction and Comparison of Difference Schemes