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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2013

On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit

Résumé

We prove an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible Euler-Poisson equation is smooth, the error between the numerical solution and the exact solution is controlled in Sobolev spaces, in a suitable phase/amplitude representation. As a corollary, we infer the numerical convergence of the quadratic observables with a time step independent of the Planck constant. A similar result is established for the nonlinear Schrodinger equation in the weakly nonlinear regime.
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Dates et versions

hal-00733128 , version 1 (18-09-2012)
hal-00733128 , version 2 (17-09-2013)

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Citer

Rémi Carles. On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit. SIAM Journal on Numerical Analysis, 2013, 51 (6), pp.3232-3258. ⟨10.1137/120892416⟩. ⟨hal-00733128v2⟩
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