Recent Advances in the Numerical Solution of Hamiltonian Partial Differential Equations

Barletti, Luigi, Brugnano, Luigi, Frasca-Caccia, Gianluca, Iavernaro, Luigi (2016) Recent Advances in the Numerical Solution of Hamiltonian Partial Differential Equations. In: AIP Conference Proceedings. 1776 (020002). pp. 1-8. IOP Institute of Physics (doi:10.1063/1.4965308) (KAR id:58071)

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Official URL: http://dx.doi.org/10.1063/1.4965308

Abstract

In this paper, we study recent results in the numerical solution of Hamiltonian partial differential equations (PDEs), 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 show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional (which derives from a proper space semi-discretization), confers more robustness to the numerical solution of such problems.

Item Type:	Conference or workshop item (Proceeding)
DOI/Identification number:	10.1063/1.4965308
Uncontrolled keywords:	Hamiltonian PDEs, HBVMs, Hamiltonian Boundary Value Methods, Energy-conserving methods, Nonlinear Schroedinger equation, Semilinear wave equation
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Gianluca Frasca-Caccia
Date Deposited:	24 Oct 2016 15:57 UTC
Last Modified:	20 May 2025 11:38 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/58071 (The current URI for this page, for reference purposes)

University of Kent Author Information

Frasca-Caccia, Gianluca.

Creator's ORCID:	https://orcid.org/0000-0002-4703-1424
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