Through the previous three editions, Handbook of Differential Equations has proven an
invaluable reference for anyone working within the field of mathematics, including …

Combinatorics and graph theory Page 2 Undergraduate Texts in Mathematics Editors S. Axler
KA Ribet For other titles published in this series, go to http://www. springer. com/series/666 …

Soliton theory is an important branch of applied mathematics and mathematical physics. An
active and productive field of research, it has important applications in fluid mechanics …

In this paper, we consider the multi-symplectic Runge–Kutta (MSRK) methods applied to the
nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi …

We present several numerical methods and establish their error estimates for the
discretization of the nonlinear Dirac equation (NLDE) in the nonrelativistic limit regime …

We consider in this paper spectral and pseudospectral approximations using Hermite
functions for PDEs on the whole line. We first develop some basic approximation results …

This paper presents a review of the current state-of-the-art of numerical methods for
nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+ 1) …

A finite difference scheme is presented for the Dirac equation in (1+ 1) D. It can handle
space-and time-dependent mass and potential terms and utilizes exact discrete transparent …

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 …

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