Singular

D.11.4 findifs_lib

Library:

findifs.lib

Purpose:

Tools for the finite difference schemes

Authors:

Viktor Levandovskyy, levandov@math.rwth-aachen.de

Overview:

We provide the presentation of difference operators in a polynomial, semi-factorized and a nodal form. Running findifs_example(); will demonstrate, how we generate finite difference schemes of linear PDEs from given approximations.

Theory: The method we use have been developed by V. Levandovskyy and Bernd Martin. The computation of a finite difference scheme of a given single linear partial differential equation with constant coefficients with a given approximation rules boils down to the computation of a Groebner basis of a submodule of a free module with respect to the ordering, eliminating module components.

Support: SpezialForschungsBereich F1301 of the Austrian FWF

Procedures:

D.11.4.1 findifs_example		containes a guided explanation of our approach
D.11.4.2 decoef		decompose polynomial P into summands with respect to the number n
D.11.4.3 difpoly2tex		present the difference scheme in the nodal form
D.11.4.4 exp2pt		convert a polynomial M into the TeX format, in nodal form
D.11.4.5 texcoef		converts the number n into TeX
D.11.4.6 npar		search for 'n' among the parameters and returns its number
D.11.4.7 magnitude		compute the square of the magnitude of a complex expression
D.11.4.8 replace		replace in s all the substrings with a given string
D.11.4.9 xchange		exchange two substrings in a given string