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@dm.unipi.it

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