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arXiv · 1209.3903

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

Rémi Carles
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Abstract

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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Rémi Carles. 2013-09-17. On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit. https://doi.org/10.1137/120892416

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