Construction of G- or G(ϵ)-symplectic general linear methods

Michal Braś, Giuseppe Izzo and Zdzislaw Jackiewicz

Applied Mathematics and Computation, 2022, vol. 431, issue C

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.

Keywords: General linear methods; Order conditions; G-symplecticness; Parasitism; Construction of methods (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322002788

DOI: 10.1016/j.amc.2022.127204

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