### 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 |  | contains 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

See also: finitediff_lib; latex_lib.

User manual for Singular version 4.4.1, 2025, generated by texi2html.