Perhaps the defining feature of waves is the fact that they propagate long distances relative
to their characteristic dimension, the wavelength. This allows us to use them to probe the …

We propose a way to efficiently treat the well-known transparent boundary conditions for the
Schrödinger equation. Our approach is based on two ideas: to write out a discrete …

This paper adresses the construction and study of a Crank-Nicolson-type discretization of
the two-dimensional linear Schrödinger equation in a bounded domain $\Omega $ with …

We present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions
for the Schrödinger equation in one dimension. The exact nonreflecting boundary condition …

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 construct a family of absorbing boundary conditions for the linear Schrödinger equation
on curved boundaries in any dimension which are local both in space and time. We give a …

This paper aims to design local absorbing boundary conditions (LABCs) for the two-
dimensional nonlinear Schrödinger equations on a rectangle by extending the unified …

We propose an adaptive approach in picking the wave-number parameter of absorbing
boundary conditions for Schrödinger-type equations. Based on the Gabor transform which …

We consider initial-boundary value problems for a generalized time-dependent Schrödinger
equation in 1D on the semi-axis and in 2D on a semi-bounded strip. For Crank-Nicolson …

When a partial differential equation in an unbounded domain is solved numerically, it is
necessary to introduce artificial boundary conditions. In this paper, a general class of …