H
amiltonian
B
oundary
V
alue
M
ethod
s
(
HBVMs
)
Energy Preserving Discrete Line Integral Methods
RECENT DEVELOPMENTS
E
nergy and
QU
adratic
I
nvariant
P
reserving (
EQUIP
) methods:
[
14
]
L.Brugnano, F.Iavernaro, D.Trigiante.
On the Existence of Energy-Preserving Symplectic Integrators Based upon Gauss Collocation Formulae
.
Preprint
, 2010 (
arXiv:
1005.1930
).
[
15
]
L.Brugnano, F.Iavernaro, D.Trigiante.
Energy and quadratic invariants preserving integrators of Gaussian type
.
AIP Conf. Proc.
1281 (2010) 227-230 (
arXiv:
1008.4790
).
<Permalink>
Numerical tests and additional theoretical achievements:
[
16
]
L.Brugnano, F.Iavernaro, D.Trigiante.
Numerical comparisons among some methods for Hamiltonian problems
.
AIP Conf. Proc
.
1281 (2010) 214-218 (
arXiv:
1008.4791
).
<Permalink>
[
17
]
L.Brugnano, F.Iavernaro, D.Trigiante.
Numerical Solution of ODEs and the Columbus' Egg: Three Simple Ideas for Three Difficult Problems
.
Mathematics in Engineering, Science and Aerospace
1, 4 (2010) 105-124 (
arXiv:
1008.
4789
).
[
18
]
L.Brugnano, F.Iavernaro, D.Trigiante.
A simple framework for the derivation and analysis of effective classes of one-step methods for ODEs
.
Applied Mathematics and Computation
218 (2012) 8475-8485
(
arXiv:
1009.3165
)
.
[
19
]
L.Brugnano, F.Iavernaro, D.Trigiante.
The Lack of Continuity and the Role of Infinite and Infnitesimal in Numerical Methods for ODEs: the Case of Symplecticity
Applied Mathematics and Computation
218 (2012) 8056-8063.
(
arXiv:
1010.4538
).
[
20
]
L.Brugnano, F.Iavernaro, D.Trigiante.
A note on the efficient implementation of Hamiltonian BVMs.
Journal of Computational and Applied Mathematics
236 (2011) 375-383
(
arXiv:
1012.2323
).
[
21
]
L.Brugnano, F.Iavernaro, D.Trigiante.
A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties.
Computer Physics Communications (accepted)
(
arXiv:
1106.0598
).
[
22
]
L.Brugnano, M.Calvo, J.I.Montijano, L.Randez.
Energy preserving methods for Poisson systems.
Journal of Computational and Applied Mathematics
doi:10.1016/j.cam.2012.02.033
[
23
]
L.Brugnano, F.Iavernaro.
Line Integral Methods which preserve all invariants of conservative problems.
Journal of Computational and Applied Mathematics
doi:10.1016/j.cam.2012.03.026
