Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity

DOI10.1137/21M1449774MaRDI QIDQ5096449

Yue Feng, Weizhu Bao, Yong-Yong Cai

Publication date: 17 August 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.14902

zbMATH Keywords

nonlinear Klein-Gordon equationlong-time dynamicstime-splitting methodsimproved uniform error boundsregularity compensation oscillation

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Numerical analysis (65-XX)

Related Items (10)

Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of 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 ⋮ Improved uniform error bounds of exponential wave integrator method for long-time dynamics of the space fractional Klein-Gordon equation with weak nonlinearity ⋮ A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials ⋮ Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant ⋮ Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Dirac equation ⋮ 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 ⋮ Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems ⋮ Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation

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