We describe the construction of G- or G(ϵ)-symplectic, and parasitism free or ϵ-parasitism free general linear methods for numerical integration of Hamiltonian systems of differential equations. Examples of such methods are presented up to the order p=4 and stage order q=p−1. Numerical experiments confirm that all methods achieve the expected order of accuracy, and that these methods approximately preserve Hamiltonians as well as quadratic invariants of differential systems.
Construction of G- or G(ϵ)-symplectic general linear methods / Bras, M.; Izzo, G.; Jackiewicz, Z.. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 431:(2022), p. 127204. [10.1016/j.amc.2022.127204]
Construction of G- or G(ϵ)-symplectic general linear methods
Izzo G.
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2022
Abstract
We describe the construction of G- or G(ϵ)-symplectic, and parasitism free or ϵ-parasitism free general linear methods for numerical integration of Hamiltonian systems of differential equations. Examples of such methods are presented up to the order p=4 and stage order q=p−1. Numerical experiments confirm that all methods achieve the expected order of accuracy, and that these methods approximately preserve Hamiltonians as well as quadratic invariants of differential systems.| File | Dimensione | Formato | |
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