57 citations · 161 across the 16 of their papers we have counts for
11 papers · 1 filter
Rigorous analysis of the time-splitting methods for the semiclassical Dirac equation
He Wang, Jia Yin
We provide rigorous error analysis of the mass-preserving time-splitting methods for solving the semiclassical Dirac equation. The scaled Planck constant in the equation gives…
A sixth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
Weiguo Gao, Zhansi He, Jia Yin
In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as , for solving the Dirac equation in the absence of external magnetic potenti…
Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials
Weizhu Bao, Yue Feng, Jia Yin
We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small electromagnetic potentials characterized by a dimen…
Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials
Yue Feng, Jia Yin
Two exponential wave integrator Fourier pseudospectral (EWI-FP) methods are presented and analyzed for the long-time dynamics of the Dirac equation with small potentials characteri…
A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials
Jia Yin
In this paper, we present an approach to deal with the dynamics of the Dirac equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting m…
Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials
Yue Feng, Jia Yin
We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic p…
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime
Ying Ma, Jia Yin
We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, in…
Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential
Weizhu Bao, Yongyong Cai, Jia Yin
Super-resolution of the Lie-Trotter splitting () and Strang splitting () is rigorously analyzed for the nonlinear Dirac equation without external magnetic potentials in t…
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime
Weizhu Bao, Yongyong Cai, Jia Yin
We establish error bounds of the Lie-Trotter splitting () and Strang splitting () for the Dirac equation in the nonrelativistic limit regime in the absence of external ma…
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
Weizhu Bao, Jia Yin
We propose a new fourth-order compact time-splitting () Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together wi…
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
Weizhu Bao, Yongyong Cai, Xiaowei Jia +1
We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a sma…