Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Peter E. Hydon"'
Autor:
Olexandr G. Rasin, Peter E. Hydon
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 1, p 026 (2005)
All three-point and five-point conservation laws for the discrete Korteweg-de Vries equations are found. These conservation laws satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. Our method us
Externí odkaz:
https://doaj.org/article/2ca2162b076045429a4a76b2d7808660
Autor:
Linyu Peng, Peter E. Hydon
The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general mappings, differe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::190df013705c7a28dec528f92ffbd1e6
Autor:
Gianluca Frasca-Caccia, Peter E. Hydon
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preser
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c628d24aed210e5ec2108792edc7999
https://kar.kent.ac.uk/88284/11/Frasca-Caccia-Hydon2021_Article_ANewTechniqueForPreservingCons.pdf
https://kar.kent.ac.uk/88284/11/Frasca-Caccia-Hydon2021_Article_ANewTechniqueForPreservingCons.pdf
Publikováno v:
Transactions of Mathematics and its Applications
We consider the calculation of Euler--Lagrange systems of ordinary difference equations, including the difference Noether's Theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We introduce the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c81dfe0f98e95cfab302d920bb800ef
https://kar.kent.ac.uk/74247/11/tnz004.pdf
https://kar.kent.ac.uk/74247/11/tnz004.pdf
Autor:
Gianluca Frasca-Caccia, Peter E. Hydon
There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of these methods preserve more than one conservation law locally. A recentl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee792ef393eab3ce75a96092e5fa50ee
http://arxiv.org/abs/1903.12278
http://arxiv.org/abs/1903.12278
Autor:
Peter E. Hydon, Gianluca Frasca-Caccia
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic nonlinearity. In p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b58608a746cb3736048dd6304e290ffe
https://hdl.handle.net/11386/4823131
https://hdl.handle.net/11386/4823131
Autor:
Peter E. Hydon, Gianluca Frasca-Caccia
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of the Euler o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b3c48fc5b8f2d9ca61576a316b1eb25
http://arxiv.org/abs/1805.03181
http://arxiv.org/abs/1805.03181
Autor:
Peter E. Hydon, Timothy J. Grant
Publikováno v:
Foundations of Computational Mathematics. 13:667-692
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove
Publikováno v:
Journal of Theoretical Biology. 286:57-66
Fine/ultrafine particles can easily reach the pulmonary acinus, where gas is exchanged, but they need to mix with alveolar residual air to land on the septal surface. Classical fluid mechanics theory excludes flow-induced mixing mechanisms because of
Autor:
Peter E. Hydon, F. E. Laine-Pearson
Publikováno v:
European Journal of Mechanics - B/Fluids. 29:278-284
Recent experiments have shown that rapid kinematic mixing occurs in the pulmonary alveoli. Here the Reynolds number is very small, there is recirculation in the alveolar cavity and the alveolar walls move periodically. We have recently shown that non