Improved uniform error bounds on an exponential wave integrator method for the nonlinear Schrödinger equation with wave operator and weak nonlinearity

DOI10.1016/j.apnum.2024.04.001MaRDI QIDQ6549568

Jiyong Li, Qianyu Chen

Publication date: 4 June 2024

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

zbMATH Keywords

long-time dynamicsweak nonlinearitynonlinear Schrödinger equation with wave operatorimproved uniform error boundsLawson-type exponential wave integrator

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Quantum theory (81-XX)

Cites Work

• Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator
• 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 nonrelativistic limits of the Klein-Gordon and Dirac equations
• 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
• Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Modeling light bullets with the two-dimensional sine-Gordon equation
• A combination of multiscale time integrator and two-scale formulation for the nonlinear Schrödinger equation with wave operator
• Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials
• A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator
• Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials
• A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with energy-preservation for long-time dynamics of the nonlinear Klein-Gordon equation
• Optimal \(l^\infty\) error estimates of the conservative scheme for two-dimensional Schrödinger equations with wave operator
• Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems
• A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials
• Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations
• Exponential integrators
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Spectral Methods
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation
• Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions
• Finite difference discretization of the cubic Schrödinger equation
• Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
• Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
• Finite Difference Method for Generalized Zakharov Equations
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• Uniform Error Bounds of an Exponential Wave Integrator for the Long-Time Dynamics of the Nonlinear Klein--Gordon Equation
• Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity
• Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of the Dirac Equation with Small Potentials
• Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity
• Long Time Error Analysis of Finite Difference Time Domain Methods for the Nonlinear Klein-Gordon Equation with Weak Nonlinearity
• Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator
• On Time-Splitting Pseudospectral Discretization for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime
• Geometric Numerical Integration
• Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
• Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
• A singular perturbation problem for an envelope equation in plasma physics
• Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant
• Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear <scp>Klein–Gordon</scp> equation with weak nonlinearity
• Improved uniform error bounds of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Schrödinger equation with the small coupling constant
• Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations

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