A Symposium on
Splitting
Methods for Differential Equations
Institut
de
Matemàtiques
i
Aplicacions
de
Castelló
(IMAC)
September 6-8, 2010
Castellón,
Spain
Splitting methods constitute
a widely used tool of the numerical integration of ordinary differential equations (ODEs). Most often they are
the option of choice when the vector field associated with the ODE can be decomposed into several
pieces and each of them is integrable. Some of the advantages
that splitting methods possess can be summarized as follows:
They are usually simple
to implement.
They are, in general,
explicit.
Their storage
requirements are quite modest. The algorithms are sequential and the
solutions at intermediate stages are stored in the solution vectors.
This property can be of great interest when they are applied to partial
differential equations (PDEs) previously semidiscretized.
There exist in the
literature a large number of specific methods tailored for different
structures.
They preserve structural
properties of the exact solution, thus conferring to the numerical
scheme a qualitative superiority with respect to other standard
integrators, especially when long time intervals are considered.
Examples of these structural features are symplecticity, volume
preservation, time-symmetry and conservation of first integrals. In
this sense, splitting methods constitute an important class of geometric numerical integrators.
In addition, the numerical
solution obtained by splitting schemes can be seen as the exact solution to a perturbed system of
ODEs possessing the same geometric properties as the original system. This backward error
interpretation has direct implications for the qualitative behaviour of the numerical solution as
well as for the error propagation along time.
The intention of the symposium is
to
provide a platform for exchanging new ideas and results in the development and analysis of splitting
methods for the time integration of both ordinary and partial differential equations.
The symposium will take place at
the
Institut
de
Matemàtiques
i
Aplicacions
de
Castelló (IMAC), Universitat Jaume I, in
Castellón (Spain). It will start on Monday September 6 and will
end on Wednesday September 8 at midday.
PARTICIPANTS
Philipp Bader (Valencia)
Philippe Chartier (Rennes)
Siu A. Chin (Texas A&M)
Stéphane Descombes (Nice)
Fasma Diele (Bari)
Erwan Faou (Rennes)
Juergen Geiser (Berlin)
M. Atakan Gurkan (Leiden)
Reinout Quispel (La Trobe)
Tim Sheng (Baylor)
Mechthild Thalhammer (Innsbruck)
Gilles Vilmart (Lausanne)
Pura Vindel (Castellón)
ORGANIZING
COMMITTEE
Sergio Blanes (Universidad
Politécnica de Valencia)
Accommodation. We have booked a
number of rooms for the participants at Hotel Luz. It is
conveniently located near the railway/bus station and TRAM stop. Just
exit the station through the north gate and cross the street.
Internet
access. You can access to the
Internet via Eduroam or via the UJI network. In the later case you will
need to instal a VPN client programme. Detailed instructions can be
found here.
You
have
the
username
and password of your account in your badge.
Institut de Matemàtiques i
Aplicacions de Castelló (IMAC).
This is a mathematical
research institute which recently initiated its activities in
Castellón.