Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator

DOI10.1016/j.jmaa.2014.08.026zbMath1300.65061OpenAlexW2055514331MaRDI QIDQ458321

Ting-chun Wang

Publication date: 7 October 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.08.026

zbMATH Keywords

convergencenonlinear Schrödinger equationnumerical resultinduction argumentpointwise error estimatereduction of order methodsemi-implicit compact finite difference methodsuniform error estimate

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• 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 three level linearized compact difference scheme for the Cahn-Hilliard equation
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
• Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
• Analysis of some new conservative schemes for nonlinear Schrödinger equation with wave operator
• Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse
• On the convergence of splitting methods for linear evolutionary Schrödinger equations involving an unbounded potential
• On the nonrelativistic limits of the Klein-Gordon and Dirac equations
• Compact finite difference schemes with spectral-like resolution
• On the numerical solution of the cubic Schrödinger equation in one space variable
• Semidiscretization in time for nonlinear Schrödinger-wave equations
• Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Modeling light bullets with the two-dimensional sine-Gordon equation
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Optimal Point-Wise Error Estimate of a Compact Finite Difference Scheme for the Coupled Nonlinear Schrödinger Equations
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation
• Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
• Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions
• A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
• Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation
• Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
• A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients
• Time Compact High Order Difference Methods for Wave Propagation
• Time Compact Difference Methods for Wave Propagation in Discontinuous Media
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction
• Analysis of a Fourth‐Order Scheme for a Three‐Dimensional Convection‐Diffusion Model Problem
• Convergence of Fourth Order Compact Difference Schemes for Three‐Dimensional Convection‐Diffusion Equations
• A singular perturbation problem for an envelope equation in plasma physics