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Operator Semigroups and Numerical Analysis (TUD) (M)

Course
2011-2012

As in previous years there is the possibility to participate in an international lecture course on a graduate level, the so-called “International Internetseminar”. The topic of the upcoming issue is “Operator Semigroups and Numerical Analysis”, on an operator theoretic and functional analytic approach to the numerical treatment of evolution equations. Operator semigroups are an infinite-dimensional version of the matrix exponential function e^{tA} common in the treatment of systems of linear ODE. When one treats partial differential equations of evolutionary type, like the well-known heat or wave equations, one can do quite the same as in the matrix case, only A will be a partial differential operator (like the Laplacian) on an infinite-dimensional space. Approximation formulae for solutions via time/space-discretization, like e.g. the well-known backward Euler method and Fourier-Galerkin methods, are one-to-one translations of limit theorems for operator semigroups. Hence the topic is an optimal example of “Applicable Functional Analysis” of evolution equations. As you can read on the website following the link to the general information below, the course has three phases, a study phase from October-February, a project preparation phase from April-May and a workshop in June where the projects are presented. A local group in Delft will be launched and meet regularly to discuss the material and the exercises. Leiden participants are welcome to join this group.

Board in Blaubeuren
In previous years the participants’ accomodation and cost of living in Phase 3 (meeting in Blaubeuren) were covered by a sponsor. At the moment of closing of this e-guide, this is under investigation.
Travel expenses
Partial support in travel expenses by the Leiden Mathematical Institute is likely to be possible.
Leiden contact
Dr. M.F.E. de Jeu
Prerequisites
Linear Analysis (Leiden course), basic familiarity with ordinary and partial differential equations and numerical analysis

Links
General information
Detailed description