IMUB UB
 

Advanced Course on
Long Time Integrations

Barcelona, September 3-7, 2007


For many differential equations it is necessary to have methods which are both accurate and fast. This need appears in long time integrations (say, of the order of $10^9$ times some characteristic time of the system) and also for moderate time intervals when massive simulations are required for global and statistical purposes. Beyond classical methods there is at present a strong interest in ``geometric'' methods which are intended to preserve some geometric and/or structural properties of the system. It is worth to discuss the suitability of different methods as a function of the problem at hand. Furthermore moderate and long time integrations are used to detect properties (regularity, chaoticity) of the system which can be done by computing Lyapunov exponents and carrying out a frequency analysis. Another purpose is the numerical computation of relevant objects such as periodic and quasiperiodic solutions, etc, to study its stability, bifurcations and continuation as a function of parameters. These computations can require a very good accuracy. Finally, with methods having a very small truncation error, the role of the propagation of round off error should be studied, specially for regular (non-chaotic) orbits.

The course will take place at Room B1, located at the ground level of the Court of Sciences (Pati de Ciencies), in the right part of the historical building of the Universitat de Barcelona (the address is at the end of this page). We will provide wifi access for the participants.

How to arrive

Lecturers
G. Gómez (U. Barcelona), À. Jorba (U. Barcelona), J. Laskar (IMCCE, Observatoire de Paris), B. Leimkuhler (Edinburgh U.), J.M. Mondelo (U. Autònoma de Barcelona), C. Simó (U. Barcelona).

Contents of the lectures
Slides and links
Carles Simˇ:No. 8 at http://www.maia.ub.es/dsg/2007/
J.M.Mondelo:Tuesday's lecture and Thursday's lecture
└ngel Jorba: Three sessions
Ben Leimkuhler:Six lectures, Local copy of the whole thing in a tar.gz file

Schedule


Monday
Tuesday
Wednesday
Thursday
Friday
09:00-10:00
Simó
Jorba
Leimkuhler
Leimkuhler
Gómez
10:00-11:00
Simó Simó
Leimkuhler
Leimkuhler
Jorba
11:00-11:30
Coffee break
Coffee break Coffee break Coffee break Coffee break
11:30-12:30
Leimkuhler
Laskar
Laskar
Laskar
Jorba
12:30-13:30
Leimkuhler
Laskar
Laskar
Laskar
Closing
13:30-15:30





15:30-16:30
Gómez
Mondelo
Jorba
Mondelo

16:30-17:00
Coffee break Coffee break Coffee break Coffee break
17:00-18:00
Gómez
Mondelo
F. Borondo2
S. Blanes3

18:00-19:00

R. Barrio1

J. Palacián4



1 Title of the talk: Polynomial series integration method and applications
2 Title of the talk: Homolclinic motions in quantum mechanics
3 Title of the talk: Composition and splitting methods
4 Title of the talk: Lunar theory: analytical vs numerical approach

Preregistration


To attend you must preregister first. To do it, click here.  As the attendance is limited, the preregistration will be closed when the course is full.

Registration

The registration fee is of 50€ for researchers belonging to the Consolider project i-MATH, and 100€ for other researchers. Details will be e-mailed to preregistered participants.

Grants

There are some grants to help with the local expenses to young students. If you are interested, mark the appropriate box when preregistering, send your CV (in pdf format) to the address lti07<at>imub.ub.es, and ask a senior researcher to e-mail a support letter to the same address, including the phone of the supporter.

Note that finantial help will be granted with the following order of priority: young researchers belonging to teams included in i-MATH, other researchers belonging to these teams, other spanish participants, non-spanish participants.

The deadline to ask for a grant is July 13. Granted students will be notified by e-mail on July 20.

Accomodation

Contact to: investigadors<at>resa.es, www.residencia-investigadors.es, www.resa.es

Make sure that the reservation is done well in advance. Otherwise it can be full.

Organizers

The organizers are Àngel Jorba and Carles Simó, with the collaboration of Ariadna Farrés and Montse Navarro. For more information, write them to the address lti07 at imub.ub.es (this address is not clickable, you should type it in your e-mail program; this has been done to minimize the amount of spam we receive).

Support

The course is supported by i-MATH (Consolider project from the Spanish Minsitry of Education and Science), IMUB and the research teams on Dynamical Systems of the UB.




Ingenio - Mathematica
MEC - CI 2010


IMUB
Institut de Matemàtica 
Gran Via de les Corts Catalanes 585,
08007 Barcelona, Spain
Email: imub@imub.ub.es
URL: www.imub.ub.es
Phone: (+34) 93 402 13 85
Fax:  (+34) 93 403 59 63

Last modified: Sept 10, 2007