Uniform Error Bounds of an Exponential Wave Integrator for the Long-Time Dynamics of the Nonlinear Klein--Gordon Equation

DOI10.1137/20M1327677zbMath1496.65178arXiv2003.11785OpenAlexW3188632119WikidataQ115525537 ScholiaQ115525537MaRDI QIDQ5006474

Yue Feng, Wenfan Yi

Publication date: 16 August 2021

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.11785

zbMATH Keywords

nonlinear Klein-Gordon equationuniform error boundsweak nonlinearitylong-time analysisGautschi-type exponential wave integrator Fourier pseudospectral method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Second-order nonlinear hyperbolic equations (35L70) 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) Electromagnetic interaction; quantum electrodynamics (81V10) Computational methods for problems pertaining to quantum theory (81-08) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (8)

A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with energy-preservation for long-time dynamics of the nonlinear Klein-Gordon equation ⋮ Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity ⋮ Time integrators for dispersive equations in the long wave regime ⋮ Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant ⋮ Improved uniform error bounds of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Schrödinger equation with the small coupling constant ⋮ Uniform Error Bound of an Exponential Wave Integrator for Long-Time Dynamics of 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 ⋮ Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity

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