Efficient semi-implicit compact finite difference scheme for nonlinear Schrödinger equations on unbounded domain

DOI10.1016/j.apnum.2020.02.014zbMath1436.65103OpenAlexW3008876361MaRDI QIDQ1986164

Ziwen Jiang, Yunxia Hu, Hong-Wei Li

Publication date: 7 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.02.014

zbMATH Keywords

unbounded domainnonlinear Schrödinger equationabsorbing boundary conditionscompact finite different scheme

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

A new absorbing layer approach for solving the nonlinear Schrödinger equation ⋮ A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local artificial boundary conditions for Schrödinger and heat equations by using high-order azimuth derivatives on circular artificial boundary
• A compact difference scheme for the fractional diffusion-wave equation
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings
• Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
• A fourth-order approximation of fractional derivatives with its applications
• A dispersion minimizing compact finite difference scheme for the 2D Helmholtz equation
• Compact finite difference method for the fractional diffusion equation
• Faithful transfer of difference boundary conditions
• Discrete transparent boundary conditions for the equation of rod transverse vibrations
• Numerical computations for \(N\)-coupled nonlinear Schrödinger equations by split step spectral methods
• Discrete transparent boundary conditions for the Schrödinger equation -- a compact higher order scheme
• Discrete artificial boundary conditions for nonlinear Schrödinger equations
• Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain
• Exact non-reflecting boundary conditions
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• A simple boundary condition for unbounded hyperbolic flows
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation.
• Semidiscretization in time for nonlinear Schrödinger-wave equations
• An optimal compact sixth-order finite difference scheme for the Helmholtz equation
• The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions
• Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation
• A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations
• Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations
• Optimal error estimate of a compact scheme for nonlinear Schrödinger equation
• Dynamics of repelling soliton collisions in coupled Schrödinger equations
• A perfectly matched layer approach to the nonlinear Schrödinger wave equations
• Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• A Padé compact high-order finite volume scheme for nonlinear Schrödinger equations
• The solvability of coupling the thermal effect and magnetohydrodynamics field with turbulent convection zone and the flow field
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
• Convergence of compact ADI method for solving linear Schrödinger equations
• ON A MIXED BOUNDARY-VALUE PROBLEM IMITATING THE CAUCHY PROBLEM
• Radiation boundary conditions for wave-like equations
• Absorbing boundary conditions for numerical simulation of waves
• Radiation boundary conditions for acoustic and elastic wave calculations
• Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation
• Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities
• Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation
• Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schrödinger Equation
• Absorbing Boundary Conditions for the Schrödinger Equation
• Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• Artificial Boundary Method
• Efficient representation of nonreflecting boundary conditions for the time‐dependent Schrödinger equation in two dimensions
• Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• A singular perturbation problem for an envelope equation in plasma physics