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 RungeâKutta 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
2017-01-01
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 RungeâKutta case to a full multivalue case. Criteria are found for eliminating parasitic behaviour and order conditions are explored.Pubblicazioni consigliate
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