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FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Ignat LI

Editorial: World Scientific Publishing Company, Mathematical Models and Methods in Applied Sciences, 17, p.567-591, 2007.

Rezumat:

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.

Cuvinte cheie: Finite differences; Fourier multipliers; Strichartz estimates; nonlinear Schrödinger equations

URL: http://www.worldscinet.com/m3as/17/1704/S0218202507002029.html