Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

DOI10.1007/s11075-021-01159-wOpenAlexW3181875108MaRDI QIDQ2118945

Jia Yin, Ying Ma

Publication date: 23 March 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.14698

zbMATH Keywords

finite difference methodDirac equationmassless and nonrelativistic regimeoscillatory in timerapid motion in space

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (3)

A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials ⋮ Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime ⋮ Explicit and structure-preserving exponential wave integrator Fourier pseudo-spectral methods for the Dirac equation in the simultaneously massless and nonrelativistic regime

Cites Work

• Unnamed Item
• Unnamed Item
• Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
• A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
• Single-cone real-space finite difference scheme for the time-dependent Dirac equation
• A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry
• Gaussian beam methods for the Dirac equation in the semi-classical regime
• An integrating factor for nonlinear Dirac equations
• Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces
• Linearized Crank-Nicolson scheme for nonlinear Dirac equations
• A semiclassical approach to the Dirac equation
• An overview on linear and nonlinear Dirac equations
• Approximating eigenvalues of Dirac system with discontinuities at several points using Hermite-Gauss method
• Computational performance of simple and efficient sequential and parallel Dirac equation solvers
• Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime
• A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials
• A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers
• Error bounds of the finite difference time domain methods for the Dirac equation in the semiclassical regime
• A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
• A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation
• Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
• A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime
• A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime
• Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime
• Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime
• Time‐splitting methods with charge conservation for the nonlinear Dirac equation
• On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

This page was built for publication: Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime