Error bounds of the finite difference time domain methods for the Dirac equation in the semiclassical regime
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Publication:2291890
DOI10.1007/s10915-019-01063-5zbMath1453.65228OpenAlexW2979799995WikidataQ127155857 ScholiaQ127155857MaRDI QIDQ2291890
Publication date: 31 January 2020
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-019-01063-5
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)
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Cites Work
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- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
- Absorbing boundary conditions for relativistic quantum mechanics equations
- Gaussian beam methods for the Dirac equation in the semi-classical regime
- On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity
- Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
- The ``electromagnetic Wigner equation for an electron with spin
- A semiclassical approach to the Dirac equation
- Semiclassical limit of the Dirac equation and spin precession.
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- Computational performance of simple and efficient sequential and parallel Dirac equation solvers
- An efficient and stable numerical method for the Maxwell--Dirac system
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime
- A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
- Wave packets in honeycomb structures and two-dimensional Dirac equations
- A time-splitting spectral scheme for the Maxwell-Dirac system
- A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime
- Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
- Mathematical and computational methods for semiclassical Schrödinger equations
- General solutions of Maxwell–Dirac equations in 1+1-dimensional space–time and a spatially confined solution
- A class of exact plane wave solutions of the Maxwell–Dirac equations
- Homogenization limits and Wigner transforms
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
- Honeycomb Schrödinger Operators in the Strong Binding Regime
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime
- Dirac equation for cold atoms in artificial curved spacetimes
- Honeycomb lattice potentials and Dirac points
- On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit
- The cauchy problem for the coupled maxwell and dirac equations