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Order estimates in time of splitting methods for the nonlinear Schrödinger equation

Abstract : In this paper, we consider the nonlinear Schrödinger equation ut + iΔu − F(u) = 0 in two dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang formulae (which are splitting methods) are approximations of the exact solution of order 1 and 2 in time.
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https://hal.archives-ouvertes.fr/hal-00319991
Contributor : Brigitte Bidégaray-Fesquet <>
Submitted on : Wednesday, June 9, 2021 - 2:21:45 PM
Last modification on : Thursday, June 10, 2021 - 1:58:57 PM

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Christophe Besse, Brigitte Bidégaray, Stéphane Descombes. Order estimates in time of splitting methods for the nonlinear Schrödinger equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2002, 40 (1), pp.26-40. ⟨10.1137/S0036142900381497⟩. ⟨hal-00319991⟩

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