TY - JOUR
T1 - A new class of G(ϵ)-symplectic general linear methods
AU - Braś, Michal
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of the first author (M. Bras) was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education.
Publisher Copyright:
© 2022 IMACS
PY - 2023/1
Y1 - 2023/1
N2 - A new class of G(ϵ)-symplectic general linear methods for numerical integration of Hamiltonian systems of differential equations is described. Order conditions for these methods are derived using Albrecht approach and the construction of G(ϵ)-symplectic method is described based on solving minimization problems with nonlinear inequality constrains. Examples of methods up to the order four are presented. Numerical experiments confirm that these methods achieve the expected order of accuracy and that they approximately preserve Hamiltonians of differential systems.
AB - A new class of G(ϵ)-symplectic general linear methods for numerical integration of Hamiltonian systems of differential equations is described. Order conditions for these methods are derived using Albrecht approach and the construction of G(ϵ)-symplectic method is described based on solving minimization problems with nonlinear inequality constrains. Examples of methods up to the order four are presented. Numerical experiments confirm that these methods achieve the expected order of accuracy and that they approximately preserve Hamiltonians of differential systems.
KW - Construction of methods
KW - G(ϵ)-symplecticness
KW - General linear methods
KW - Order conditions
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U2 - 10.1016/j.apnum.2022.08.010
DO - 10.1016/j.apnum.2022.08.010
M3 - Article
AN - SCOPUS:85137167872
SN - 0168-9274
VL - 183
SP - 1
EP - 14
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -