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FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

LIVIU I. IGNAT

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

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

https://doi.org/10.1142/S0218202507002029Cited by:13 (Source: Crossref)

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.

Keywords:

AMSC: 65M12, 42A45, 35Q55

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