Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D

DOI10.1016/j.cam.2016.12.004zbMath1357.65148OpenAlexW2561188040MaRDI QIDQ508046

Jilu Wang, Sun, Weiwei

Publication date: 9 February 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.12.004

zbMATH Keywords

numerical examplesfinite difference schemescoupled nonlinear Schrödinger systemunconditionally optimal error estimatesemi-implicit Crank-Nicolson schemes

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the \(L_\infty \) convergence of a difference scheme for coupled nonlinear Schrödinger equations
• New conservative difference schemes for a coupled nonlinear Schrödinger system
• Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials
• A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
• A robust semi-explicit difference scheme for the Kuramoto-Tsuzuki equation
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• Finite element approximation for the viscoelastic fluid motion problem
• On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations
• Self-similarity and asymptotic stability for coupled nonlinear Schrödinger equations in high dimensions
• The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
• Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
• Stability Analysis of Multipulses in Nonlinearly-Coupled Schrodinger Equations
• On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
• A modified numerical scheme for the cubic Schrödinger equation
• Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
• Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Multilevel Spectral-Galerkin and Continuation Methods for Nonlinear Schrödinger Equations
• Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
• Stability Analysis of Difference Schemes for Variable Coefficient Schrödinger Type Equations
• Optimal H¹ Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
• Convergence of an Energy-Preserving Scheme for the Zakharov Equations in one Space Dimension
• An Unconditionally Stable Three-Level Explicit Difference Scheme for the Schrödinger Equation with a Variable Coefficient
• Three-Level Galerkin Methods for Parabolic Equations
• On Convergence and Stability of the Explicit Difference Method for Solution of Nonlinear Schrödinger Equations
• Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
• Finite Difference Method for Generalized Zakharov Equations
• Stability of solitary waves for coupled nonlinear schrödinger equations
• Dufort–Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations
• Error Estimates of Splitting Galerkin Methods for Heat and Sweat Transport in Textile Materials
• Numerical simulation of coupled nonlinear Schrödinger equation