Partitioned general linear methods possessing the G-symplecticity property are introduced. These are intended for the numerical solution of separable Hamiltonian problems and, as for multivalue methods in general, there is a potential for loss of accuracy because of parasitic solution growth. The solution of mechanical problems over extended time intervals often benefits from interchange symmetry as well as from symplectic behaviour. A special type of symmetry, known as interchange symmetry, is developed from a model Runge–Kutta case to a full multivalue case. Criteria are found for eliminating parasitic behaviour and order conditions are explored.

Partitioned general linear methods for separable Hamiltonian problems

D'AMBROSIO, RAFFAELE
2017

Abstract

Partitioned general linear methods possessing the G-symplecticity property are introduced. These are intended for the numerical solution of separable Hamiltonian problems and, as for multivalue methods in general, there is a potential for loss of accuracy because of parasitic solution growth. The solution of mechanical problems over extended time intervals often benefits from interchange symmetry as well as from symplectic behaviour. A special type of symmetry, known as interchange symmetry, is developed from a model Runge–Kutta case to a full multivalue case. Criteria are found for eliminating parasitic behaviour and order conditions are explored.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4683106
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