Low-regularity integrators for nonlinear Dirac equations

K Schratz, Y Wang, X Zhao - Mathematics of Computation, 2021 - ams.org
In this work, we consider the numerical integration of the nonlinear Dirac equation and the
Dirac–Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity …

Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity

W Bao, Y Feng, C Su - Mathematics of Computation, 2022 - ams.org
We establish uniform error bounds of time-splitting Fourier pseudospectral (TSFP) methods
for the nonlinear Klein–Gordon equation (NKGE) with weak power-type nonlinearity and $ O …

Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling …

J Li, X Jin - Numerical Methods for Partial Differential …, 2023 - Wiley Online Library
Recently, the numerical methods for long‐time dynamics of PDEs with weak nonlinearity (or
small potentials) have received more and more attention. For the Klein‐Gordon‐Dirac (KGD) …

Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation

J Li - Mathematics and Computers in Simulation, 2023 - Elsevier
Recently, a time-splitting Fourier pseudo-spectral (TSFP) scheme for solving numerically the
Klein–Gordon–Dirac equation (KGDE) has been proposed (Yi et al., 2019). However, that …

Analysis of a conservative fourth-order compact finite difference scheme for the Klein–Gordon–Dirac equation

J Li, T Wang - Computational and Applied Mathematics, 2021 - Springer
In this paper, we propose and analyze a conservative fourth-order compact finite difference
scheme for the Klein–Gordon–Dirac equation with periodic boundary conditions. Based on …

Uniform Error Bounds of an Exponential Wave Integrator for the Long-Time Dynamics of the Nonlinear Klein--Gordon Equation

Y Feng, W Yi - Multiscale Modeling & Simulation, 2021 - SIAM
We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral
(EWI-FP) method for the long-time dynamics of the nonlinear Klein--Gordon equation …

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

J Li - Numerical Methods for Partial Differential Equations, 2024 - Wiley Online Library
We provide improved uniform error estimates for the time‐splitting Fourier pseudo‐spectral
(TSFP) methods applied to the Klein–Gordon–Dirac system (KGDS) with the small …

Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation

J Li - Mathematics and Computers in Simulation, 2021 - Elsevier
Recently, an exponential integrator Fourier pseudo-spectral (EIFP) scheme for the Klein–
Gordon–Dirac (KGD) equation in the nonrelativistic limit regime has been proposed (Yi et …

Two energy-preserving Fourier pseudo-spectral methods and error estimate for the Klein–Gordon–Dirac system

F Liao, F Geng, T Wang - … in Nonlinear Science and Numerical Simulation, 2023 - Elsevier
We devote the present paper to the convergency of conservative Fourier pseudo-spectral
methods for three-dimensional Klein–Gordon–Dirac (KGD) system. By adopting the …

Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac system

X Wang, J Li - Applied Mathematics and Computation, 2023 - Elsevier
In this paper, we propose and study two conservative finite difference Fourier pseudo-
spectral schemes numerically solving the Klein-Gordon-Dirac (KGD) system with periodic …