We analyze rigorously error estimates and compare numerically spatial/temporal resolution
of various numerical methods for the discretization of the Dirac equation in the nonrelativistic …

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 …

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 …

This paper is devoted to the construction and analysis of uniformly accurate nested Picard
iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit regime. In this …

We develop improved uniform error bounds on a second-order Strang splitting method for
the long-time dynamics of the nonlinear space fractional Dirac equation (NSFDE) in two …

We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral
(MTI-FP) method for the (linear) Dirac equation with a dimensionless parameter ε∈(0,1 …

Pseudospectral numerical schemes for solving the Dirac equation in general static curved
space are derived using a new pseudodifferential representation of the Dirac equation along …

We propose a new fourth-order compact time-splitting (S_ 4c S 4 c) Fourier pseudospectral
method for the Dirac equation by splitting the Dirac equation into two parts together with …

A multiscale time integrator Fourier pseudospectral (MTI-FP) method is proposed and
rigorously analyzed for the nonlinear Dirac equation (NLDE), which involves a …

We establish error bounds of the Lie-Trotter splitting ($ S_1 $) and Strang splitting ($ S_2 $)
for the Dirac equation in the nonrelativistic regime in the absence of external magnetic …