Mikhail Shashkov
Group T-7, Los Alamos National Laboratory, MS-B284,
Los Alamos, NM  87544 USA

V.G.Ganzha
GH-Universitat, Kassel, Germany


 Using the Symbolic Computation for Analysis of Local Approximation
of Finite-Difference Operators


                       Abstract

  The construction and investigation of finite-difference schemes on irregular
grid for multidimensional equations of mathematical physics involves the
processing of great amount of symbolic information. An attempt to do this
manipulation by hand on the paper may lead to errors. Therefore, the problem of
the construction of the algorithms for solving these problems which would
allow the application of computers for their implementation is important.

In this lecture algorithms allowing to investigate the  order local
approximation of finite-difference operators on the class of sufficiently
smooth functions are considered. The case of arbitrary computational mesh
and of an arbitrary number of spatial dimensions are considered. The
grid must satisfy some natural regularity conditions.

Examples of investigation of approximation for particular finite-difference
operators in case of one ore two spatial variables are given.