Energy preserving methods for nonlinear schrodinger equations

Abstract : This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schrödinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods.
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Contributor : Guillaume Dujardin <>
Submitted on : Tuesday, December 11, 2018 - 4:36:00 PM
Last modification on : Monday, April 29, 2019 - 4:33:08 PM
Long-term archiving on : Tuesday, March 12, 2019 - 2:41:13 PM


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  • HAL Id : hal-01951527, version 1


Christophe Besse, Stephane Descombes, Guillaume Dujardin, Ingrid Lacroix-Violet. Energy preserving methods for nonlinear schrodinger equations. 2018. ⟨hal-01951527⟩



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