A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime

DOI10.1137/130950665zbMath1310.65131arXiv1401.0984OpenAlexW4232654152MaRDI QIDQ5174905

Weizhu Bao, Xiaofei Zhao, Yong-Yong Cai

Publication date: 19 February 2015

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

Full work available at URL: https://arxiv.org/abs/1401.0984

zbMATH Keywords

nonlinear Schrödinger equationKlein-Gordon equationerror boundquadratic convergencelinear convergencespectral methodexponential convergencenonrelativistic limitFourier pseudospectral methodnumerical resultexponential wave integratormultiscale decompositionmeshing strategymultiscale time integratoruniformly accurate

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) 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)

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