n this paper we review some basic facts concerning the class of Line Integral Methods, recently defined for numerically solving conservative problems. The main instance of such methods is given by Hamiltonian Boundary Value Methods (HBVMs), a class of energy-conserving Runge-Kutta methods for Hamiltonian problems, which are here recalled. Also, we sketch some recent extensions and generalizations.
Recent advances in geometric numerical integration / Brugnano, Luigi; Gurioli, Gianmarco; Iavernaro, Felice. - In: AIP CONFERENCE PROCEEDINGS. - ISSN 0094-243X. - ELETTRONICO. - 3315:(2025), pp. 0200021-0200027. (Intervento presentato al convegno INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2023 tenutosi a Heraklion, Greece nel 11–17 September 2023) [10.1063/5.0286078].
Recent advances in geometric numerical integration
Brugnano, Luigi;Gurioli, Gianmarco;
2025
Abstract
n this paper we review some basic facts concerning the class of Line Integral Methods, recently defined for numerically solving conservative problems. The main instance of such methods is given by Hamiltonian Boundary Value Methods (HBVMs), a class of energy-conserving Runge-Kutta methods for Hamiltonian problems, which are here recalled. Also, we sketch some recent extensions and generalizations.
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