Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
MATHEMATICS OF COMPUTATION Volume 73, Number 248, Pages 17791799
 

Summary: MATHEMATICS OF COMPUTATION
Volume 73, Number 248, Pages 1779­1799
S 0025-5718(04)01631-X
Article electronically published on January 23, 2004
NUMERICAL SCHEMES FOR THE SIMULATION
OF THE TWO-DIMENSIONAL SCHR¨ODINGER EQUATION
USING NON-REFLECTING BOUNDARY CONDITIONS
XAVIER ANTOINE, CHRISTOPHE BESSE, AND VINCENT MOUYSSET
Abstract. This paper adresses the construction and study of a Crank-Nicol-
son-type discretization of the two-dimensional linear Schr¨odinger equation in
a bounded domain with artificial boundary conditions set on the arbitrarily
shaped boundary of . These conditions present the features of being differ-
ential in space and nonlocal in time since their definition involves some time
fractional operators. After having proved the well-posedness of the continuous
truncated initial boundary value problem, a semi-discrete Crank-Nicolson-type
scheme for the bounded problem is introduced and its stability is provided.
Next, the full discretization is realized by way of a standard finite-element
method to preserve the stability of the scheme. Some numerical simulations
are given to illustrate the effectiveness and flexibility of the method.
1. Introduction

  

Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1

 

Collections: Mathematics