FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES-Reference-Cited by-同舟云学术

FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

Published:2007-04 Issue:04 Volume:17 Page:567-591
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

IGNAT LIVIU I.¹²

Affiliation:

1. Departamento de Matemáticas, Universidad Autónoma de Madrid, Crt. Colmenar Viejo, km. 15, Madrid, 28049, Spain

2. Institute of Mathematics, "Simion Stoilow" of the Romanian Academy, P. O. Box 1-764, RO-014700, Bucharest, Romania

Abstract

We consider fully discrete schemes for the one-dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular, Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent scheme for the nonlinear Schrödinger equation with nonlinearities which cannot be treated by energy methods.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202507002029

Reference27 articles.

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