Oberwolfach Seminar: Geometric Numerical Integration

Date:

November 23rd - November 29th, 2008

Organizers:

Ernst Hairer, Geneve

Marlis Hochbruck, Düsseldorf

Arieh Iserles, Cambridge

Christian Lubich, Tübingen

Programme:

Geometric numerical integration is an active interdisciplinary research area. The motivation for developing structure-preserving algorithms for special classes of differential equations originates from diverse areas such as astronomy, molecular dynamics, mechanics, control theory, theretical physics and numerical analysis, with important contributions form applied and pure mathematics. This seminar mainly adresses the numerical treatment of classes of ordinary differential equations by geometric integrators: symplectic methods for Hamiltonian problems, symmetric methods for reversible systems, methods preserving first integrals and numerical methods on manifolds.

Topics treated in the seminar will be:

• construction and discussion of geometric integrators (symplectic, symmetric, splitting, composition,...)
• backward error analysis and long-time behaviour of numerical integrators (near energy conservation, linear error growth for integrable systems, Hamiltonian perturbation theory, ...)
• treatment of differential equations on manifolds (Lie groups, constrained mechanical systems)
• differential equations with highly oscillatory solutions (modulated Fourier expansion, wave equation, exponential integrators)

The seminar will be organized in such a way that besides introductory lectures the participants have the possibility to work actively on theoretical and practical exercises.

Prerequisites:

Basic knowledge in numerical analysis and ordinary differential equations

Literature:

E. Hairer, Ch. Lubich, G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin, 2002, 2nd edition 2006.

A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett & A. Zanna, Lie-group methods, Acta Numerica 9, 2000, 215-365.

B. Leimkuhler, S. Reich, Simulating Hamiltonian Dynamics. Cambridge University Press, 2004.

Deadline for applications:

October 1, 2008

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.