Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential

DOI10.1137/19M1271828zbMath1462.35318arXiv1906.11101OpenAlexW3127420347MaRDI QIDQ4986820

Jia Yin, Weizhu Bao, Yong-Yong Cai

Publication date: 28 April 2021

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

Full work available at URL: https://arxiv.org/abs/1906.11101

zbMATH Keywords

nonlinear Dirac equationsuperresolutiontime-splittinguniform error boundnonrelativistic regime

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (8)

Improved Uniform Error Bounds on Time-Splitting Methods for the Long-Time Dynamics of the Dirac Equation with Small Potentials ⋮ Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials ⋮ Time-dependent Dirac equation with physics-informed neural networks: computation and properties ⋮ Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime ⋮ Numerical Methods for the Nonlinear Dirac Equation in the Massless Nonrelativistic Regime ⋮ On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation ⋮ Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials ⋮ Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation

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