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Journal Articles IMA Journal of Numerical Analysis Year : 2021

Energy preserving methods for nonlinear Schrödinger 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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Dates and versions

hal-01951527 , version 1 (11-12-2018)

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Cite

Christophe Besse, Stephane Descombes, Guillaume Dujardin, Ingrid Lacroix-Violet. Energy preserving methods for nonlinear Schrödinger equations. IMA Journal of Numerical Analysis, 2021, 41 (1), pp.618-653. ⟨10.1093/imanum/drz067⟩. ⟨hal-01951527⟩
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