Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Gianluca Frasca-Caccia"'
Publikováno v:
Fractional Calculus and Applied Analysis. 25:1459-1483
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have conservation laws t
Publikováno v:
Mathematics, Vol 7, Iss 3, p 275 (2019)
In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we con
Externí odkaz:
https://doaj.org/article/fb63dda77fbc407d9801666d0045d065
Publikováno v:
Computational Science and Its Applications – ICCSA 2022 ISBN: 9783031105210
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dacb714cbb8b726a30e78aaa144cd16c
https://doi.org/10.1007/978-3-031-10522-7_4
https://doi.org/10.1007/978-3-031-10522-7_4
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is further extended
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::60cb3d48812d9710161c774310086dc2
http://arxiv.org/abs/2106.01926
http://arxiv.org/abs/2106.01926
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
Autor:
Dajana Conte, Gianluca Frasca-Caccia
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when applied to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19cfb55e2ba2f0a4bef7f2546631e146
http://hdl.handle.net/11386/4769534
http://hdl.handle.net/11386/4769534
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:
Gianluca Frasca-Caccia
Publikováno v:
AIP Conference Proceedings.
Conservation laws are among the most fundamental geometric properties of a given partial differential equation. However, standard finite difference approximations rarely preserve more than a single conservation law. A novel symbolic-numerical approac
Publikováno v:
Mathematics, Vol 7, Iss 3, p 275 (2019)
In this paper, we report about recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::830f393fe749e6ccee21a103029d52e1
http://hdl.handle.net/2158/1151146
http://hdl.handle.net/2158/1151146