Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime

DOI10.1137/18M121931XzbMath1421.35307WikidataQ127541400 ScholiaQ127541400MaRDI QIDQ5232299

Yan Wang, Yong-Yong Cai

Publication date: 2 September 2019

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

zbMATH Keywords

error boundDirac equationspectral methodhigh-order accuracyexponential wave integratornonrelativistic limit regimeuniformly accurate

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) 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 (15)

A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials ⋮ Stationary state computation for nonlinear Dirac operators ⋮ Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime ⋮ Uniformly accurate nested Picard iterative integrators for the Klein-Gordon equation in the nonrelativistic regime ⋮ Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations ⋮ Uniformly accurate nested Picard iterative schemes for nonlinear Schrödinger equation with highly oscillatory potential ⋮ Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations ⋮ Super-resolution of time-splitting methods for the Dirac equation in the 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 ⋮ Low-regularity integrators for nonlinear Dirac equations ⋮ 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 Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential ⋮ On nested Picard iterative integrators for highly oscillatory second-order differential equations ⋮ Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

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