Numerical Problems of Mathematical Physics

Organizers

• V.G. Ganzha (ganzha@hrz.uni-kassel.de)
  University of Kassel
  Kassel D-34127
  Germany

• E.V. Vorozhtsov (adm@itam.nsk.su)
  Institute of Theoretical and Applied Mechanics
  Russian Academy of Sciences
  Novosibirsk 630090
  Russia

Description

The computer algebra systems (CAS's) were previously developed mainly for ensuring a possibility for symbolic computations on a computer. However, the powerful CAS's developed in recent years have also a big set of built-in functions for high-precision numerical computations. In comparison with the conventional languages for numerical computations, such as FORTRAN and C, the CAS's have considerable advantages, since they enable one to perform numerical computations, necessary analytic investigations, and to visualize the obtained results within the framework of the same computer algebra system.

The main purpose of the proposed session is the demonstration of the capabilities of advanced CAS when solving numerically the mathematics physics problems, in particular, the problems governed by partial differential equations.

Talks

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Victor G. Ganzha, K. Schaub, Evgenii V. Vorozhtsov
The Use of Mathematica for Computation of Stability Regions with Guaranteed Accuracy
Abstract

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Victor G. Ganzha, Evgenii V. Vorozhtsov
Curvilinear Grid Topology Effect on the Stability of Difference Schemes
Abstract

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Hans-Joachim Bungartz
Rapid Prototyping for the Construction of Higher Order Finite Element Methods on Sparse Grids
Abstract

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Jean-Antoine Désidéri, Margarita Spiridonova
Symbolic Computation of Linear and Nonlinear Modified (Partial Differential) Equations.
Abstract