Hamiltonian Boundary Value Methods are one step schemes of high order where the internal stages are partly exploited to impose the order conditions (fundamental stages) and partly to confer the formula the property of conserving the Hamiltonian function when this is a polynomial with a given degree v. The term "silent stages" has been coined for these latter set of extra-stages to mean that their presence does not cause an increase of the dimension of the associated nonlinear system to be solved at each step. By considering a specific method in this class, we give some details about how the solution of the nonlinear system may be conveniently carried out and how to compensate the effect of roundoff errors.

Hamiltonian BVMs (HBVMs): implementation details and applications / L.Brugnano; F.Iavernaro; T.Susca. - In: AIP CONFERENCE PROCEEDINGS. - ISSN 0094-243X. - STAMPA. - 1168:(2009), pp. 723-726. (Intervento presentato al convegno ICNAAM 2009 tenutosi a Rethymno, Crete (Greece) nel 18-22 September 2009) [10.1063/1.3241568].

Hamiltonian BVMs (HBVMs): implementation details and applications

BRUGNANO, LUIGI;
2009

Abstract

Hamiltonian Boundary Value Methods are one step schemes of high order where the internal stages are partly exploited to impose the order conditions (fundamental stages) and partly to confer the formula the property of conserving the Hamiltonian function when this is a polynomial with a given degree v. The term "silent stages" has been coined for these latter set of extra-stages to mean that their presence does not cause an increase of the dimension of the associated nonlinear system to be solved at each step. By considering a specific method in this class, we give some details about how the solution of the nonlinear system may be conveniently carried out and how to compensate the effect of roundoff errors.
2009
Proceedings of ICNAAM 2009
ICNAAM 2009
Rethymno, Crete (Greece)
18-22 September 2009
L.Brugnano; F.Iavernaro; T.Susca
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/360634
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