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

Michal Braś; Giuseppe Izzo; Zdzislaw Jackiewicz

doi:10.1016/j.amc.2022.127204

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

Michal Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Article number	127204
Journal	Applied Mathematics and Computation
Volume	431
DOIs	https://doi.org/10.1016/j.amc.2022.127204
State	Published - Oct 15 2022

Keywords

Construction of methods
G-symplecticness
General linear methods
Order conditions
Parasitism

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2022.127204

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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.",

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AU - Braś, Michal

AU - Izzo, Giuseppe

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: The authors wish to express their gratitude to anonymous reviewer for useful comments which helped to improve the presentation of the paper. Publisher Copyright: © 2022 Elsevier Inc.

PY - 2022/10/15

Y1 - 2022/10/15

N2 - 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.

AB - 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.

KW - Construction of methods

KW - G-symplecticness

KW - General linear methods

KW - Order conditions

KW - Parasitism

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JO - Applied Mathematics and Computation

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ER -

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

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Keywords

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