Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles IMA Journal of Numerical Analysis Year : 2021

Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation

Abstract

We carry out the convergence analysis of the Scalar Auxiliary Variable (SAV) method applied to the nonlinear Schrödinger equation which preserves a modified Hamiltonian on the discrete level. We derive a weak and strong convergence result, establish second-order global error bounds and present long time error estimates on the modified Hamiltonian. In addition, we illustrate the favorable energy conservation of the SAV method compared to classical splitting schemes in certain applications.
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Dates and versions

hal-03088926 , version 1 (27-12-2020)
hal-03088926 , version 2 (06-07-2021)

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Cite

Alexandre Poulain, Katharina Schratz. Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation. IMA Journal of Numerical Analysis, 2021, ⟨10.1093/imanum/drab082⟩. ⟨hal-03088926v2⟩
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