Low-regularity integrators for nonlinear Dirac equations
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 …
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
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 …
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) …
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 …
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
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 …
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
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 …
(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 …
(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 …
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 …
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 …
spectral schemes numerically solving the Klein-Gordon-Dirac (KGD) system with periodic …