[CvGmt News] [Notiziario] [Settimanale] AVVISI DI SEMINARI

[Giulia Curciarello]

martedi' - 06-04-2004 (17:00 - Sala Riunioni) :
Vladimir Gerdt

Involutive Bases and Differential Equations
argomento:non specificato

abstract:
In this talk we present the basic ideas and concepts of the involutivity
analysis of differential equation systems which goes back to the classical
Cauchy-Kovalevskaya theorem. As a specialization of these concepts to
polynomial systems we consider involutive bases of polynomial ideals.
These bases are nothing else then (generally redundant) Groebner bases and
we confront the involutive algorithm and the Buchberger algorithm in their
simplest forms. As an illustration of application of differential
involutive bases we reveal the structure of functional arbitrariness in the
general analytical solution of the two-dimensional Navier-Srokes equations
for an imcompressible fluid.

giovedi' - 15-04-2004 (17:00 - Sala Seminari) :
Vladimir Gerdt

Algorithmic Generation of Finite Difference Schemes for Differential
Equations
argomento:non specificato
abstract:

We present an algorithmic technique for construction of fully conservative
finite difference schemes for partial differential equations. This technique
based on discretization of the initial equation in its conservation law form
together with some extra integral relations. It yields an algebraic system
for
discrete values of the sought functions and its derivatives. The difference
scheme is obtained by elimination of the derivatives what can be done by
construction of an appropriate pure algebraic Groebner or involutive basis.
We demonstrate the technique by the classical Laplace equation, heat
equation and wave equation. As a nontrivial example we consider also
nonlinear Falkowich-Karman equation describing transonic flow in gas
dynamics.





Giulia Curciarello
Segreteria Didattica
tel: 050-2213219
e-mail curciare at dm.unipi.it

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