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Barletti, Luigi; Brugnano, Luigi; Frasca-Caccia, Gianluca; Iavernaro, Luigi (2016)
Publisher: IOP Institute of Physics
Languages: English
Types: Unknown
Subjects: Hamiltonian Partial Differential Equations, semilinear wave equation, nonlinear Schoedinger equation, Hamiltonian Boundary Value Methods, energy-conserving methods, QA297

Classified by OpenAIRE into

arxiv: Mathematics::Numerical Analysis
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.
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