A splitting method for the nonlinear Schrödinger equation |
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| Authors: | Liviu I. Ignat |
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| Affiliation: | a Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
b BCAM - Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500 Derio, Basque Country, Spain |
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| Abstract: | We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical well-posedness L2(Rd)-theory. More precisely, we prove that the scheme is of first order in the L2(Rd)-norm for H2(Rd)-initial data. |
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| Keywords: | 35Q55 65M15 |
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