We propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP)
method for solving the Klein--Gordon (KG) equation with a dimensionless parameter …

We introduce efficient and robust exponential-type integrators for Klein-Gordon equations
which resolve the solution in the relativistic regime as well as in the highly-oscillatory …

Different efficient and accurate numerical methods have recently been proposed and
analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter …

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 …

A multiscale time integrator Fourier pseudospectral (MTI-FP) method is proposed and
analyzed for solving the Klein–Gordon–Schrödinger (KGS) equations in the nonrelativistic …

We present the fourth‐order compact finite difference (4cFD) discretizations for the long time
dynamics of the nonlinear Klein–Gordon equation (NKGE), while the nonlinearity strength is …

In this paper, Particle-in-Cell algorithms for the Vlasov–Poisson system are presented based
on its Poisson bracket structure. The Poisson equation is solved by finite element methods …

We establish error bounds of the finite difference time domain (FDTD) methods for the long
time dynamics of the nonlinear Klein-Gordon equation (NKGE) with a cubic nonlinearity …

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 …

A multiscale time integrator sine pseudospectral (MTI-SP) method is presented for
discretizing the Klein–Gordon–Zakharov (KGZ) system with a dimensionless parameter 0< …