A new absorbing layer approach for solving the nonlinear Schrödinger equation

DOI10.1016/j.apnum.2023.04.003OpenAlexW4362705450MaRDI QIDQ6106956

Feng Guo, Weizhong Dai

Publication date: 3 July 2023

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2023.04.003

zbMATH Keywords

stabilityconvergenceinterfacefinite difference schemenonlinear Schrödinger equation

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Related Items (1)

Model and numerical method for soliton propagation through thermal medium based on nonlinear Schrödinger and heat transfer equations

Cites Work

• Unnamed Item
• Unnamed Item
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• On the accuracy of finite difference methods for elliptic problems with interfaces.
• On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
• Domain decomposition method and high-order absorbing boundary conditions for the numerical simulation of the time dependent Schrödinger equation with ionization and recombination by intense electric field
• Numerical analysis of blood flow in the heart
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation.
• High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
• A boundary condition capturing method for Poisson's equation on irregular domains
• Efficient semi-implicit compact finite difference scheme for nonlinear Schrödinger equations on unbounded domain
• Accurate gradient preserved method for solving heat conduction equations in double layers
• Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
• Open boundaries for the nonlinear Schrödinger equation
• Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems
• Absorbing boundary conditions for nonlinear scalar partial differential equations
• A perfectly matched layer approach to the nonlinear Schrödinger wave equations
• On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems
• The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• Strong coupling of Schrödinger equations: conservative scheme approach
• Gradient preserved method for solving heat conduction equation with variable coefficients in double layers
• A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain
• Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
• A new higher‐order accurate numerical method for solving heat conduction in a double‐layered film with the neumann boundary condition
• A second-order finite difference scheme for solving the dual-phase-lagging equation in a double-layered nanoscale thin film
• Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
• Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
• Dark solitons in atomic Bose–Einstein condensates: from theory to experiments
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Convergence of the ghost fluid method for elliptic equations with interfaces
• Discrete Absorbing Boundary Conditions for Schrödinger-Type Equations. Construction and Error Analysis
• Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation
• Ground States and Dynamics of Multicomponent Bose--Einstein Condensates
• The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs
• Convergence analysis of the immersed interface method
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains
• A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and Its Application to the Nonlinear Schrödinger Equation
• Generalized finite-difference time-domain method with absorbing boundary conditions for solving the nonlinear Schrödinger equation on a GPU

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