In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space–time accuracy.
Recent advances in the numerical solution of the Nonlinear Schrödinger Equation / Barletti, Luigi; Brugnano, Luigi; Gurioli, Gianmarco; Iavernaro, Felice. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 445:(2024), pp. 115826.1-115826.20. [10.1016/j.cam.2024.115826]
Recent advances in the numerical solution of the Nonlinear Schrödinger Equation
Barletti, Luigi;Brugnano, Luigi
;Gurioli, Gianmarco;
2024
Abstract
In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space–time accuracy.File | Dimensione | Formato | |
---|---|---|---|
1-s2.0-S037704272400075X-main.pdf
accesso aperto
Descrizione: file pubblicato
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Open Access
Dimensione
1.82 MB
Formato
Adobe PDF
|
1.82 MB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.