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Energy-conserving methods for the nonlinear Schrödinger equation

Barletti, L., Brugnano, L., Frasca Caccia, G., Iavernaro, F. (2017) Energy-conserving methods for the nonlinear Schrödinger equation. Applied Mathematics and Computation, 318 . pp. 3-18. ISSN 0096-3003. (doi:10.1016/j.amc.2017.04.018) (KAR id:61702)

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https://doi.org/10.1016/j.amc.2017.04.018

Abstract

In this paper, we further develop recent results in the numerical solution of Hamiltonian partial differential equations (PDEs) (Brugnano et al., 2015), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrödinger equation (NLSE), of interest in many applications. We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional, confers more robustness on the numerical solution of such a problem.

Item Type: Article
DOI/Identification number: 10.1016/j.amc.2017.04.018
Uncontrolled keywords: Hamiltonian partial differential equations; Nonlinear Schrödinger equation; Energy-conserving methods; Line integral methods; Hamiltonian Boundary Value methods; HBVMs
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Gianluca Frasca-Caccia
Date Deposited: 11 May 2017 15:18 UTC
Last Modified: 16 Feb 2021 13:45 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61702 (The current URI for this page, for reference purposes)
Frasca Caccia, G.: https://orcid.org/0000-0002-4703-1424
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