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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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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
Divisions: 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: 16 Feb 2021 13:38 UTC
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