TY - JOUR
T1 - A Wigner-measure analysis of the Dufort-Frankel scheme for the Schrošdinger equation
AU - Markowich, Peter
AU - Pietra, Paola
AU - Pohl, Carsten
AU - Stimming, Hans-Peter
N1 - Zeitschrift: SIAM Journal on Numerical Analysis
DOI: 10.1137/S0036142900381734
Coden: SJNAA
Affiliations: Institut für Mathematik, Universität Wien, Boltzmanngasse 9, A-1090 Wien, Austria; Ist. di Analisi Numerica del C.N.R., Via Ferrata 1, I-27100 Pavia, Italy; SAP AG, Neurottstrasse 16, D-69190 Walldorf, Germany
Adressen: Markowich, P.A.; Institut für Mathematik; Universität Wien; Boltzmanngasse 9 A-1090 Wien, Austria; email: [email protected]
Source-File: 506Scopus.csv
Import aus Scopus: 2-s2.0-0141645582
Importdatum: 24.01.2007 11:27:10
22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter)
04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)
PY - 2002
Y1 - 2002
N2 - We apply Wigner transform techniques to the analysis of the Dufort-Frankel difference scheme for the Schrošdinger equation and to the continuous analogue of the scheme in the case of a small (scaled) Planck constant (semiclassical regime). In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether or not caustics develop. Numerical test examples are presented to help interpret the theory and to compare the Dufort-Frankel scheme to other difference schemes for the Schrošdinger equation.
AB - We apply Wigner transform techniques to the analysis of the Dufort-Frankel difference scheme for the Schrošdinger equation and to the continuous analogue of the scheme in the case of a small (scaled) Planck constant (semiclassical regime). In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether or not caustics develop. Numerical test examples are presented to help interpret the theory and to compare the Dufort-Frankel scheme to other difference schemes for the Schrošdinger equation.
U2 - 10.1137/S0036142900381734
DO - 10.1137/S0036142900381734
M3 - Article
SN - 0036-1429
VL - 40
SP - 1281
EP - 1310
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 4
ER -