On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I

B Ducomet, A Zlotnik - 2006 - projecteuclid.org
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 …

Discrete absorbing boundary conditions for Schrödinger-type equations. construction and error analysis

I Alonso-Mallo, N Reguera - SIAM Journal on numerical Analysis, 2003 - SIAM
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 …

[PDF][PDF] On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. Part II

B Ducomet, A Zlotnik - Communications in Mathematical Sciences, 2007 - projecteuclid.org
We continue to consider initial-boundary value problems for a generalized timedependent
Schrödinger equation in 1D on the semi-axis and in 2D on a semi-bounded strip. The Crank …

Analysis of a third-order absorbing boundary condition for the Schrödinger equation discretized in space

N Reguera - Applied mathematics letters, 2004 - Elsevier
In this paper, we consider the semidiscrete problem obtained when the Schrödinger
equation is discretized in space with finite differences and a third-order absorbing boundary …