### D.15.6 finitediff_lib

Issues:

- installation of qepcadfilter.pl needs to be solved
- tests for (nearly) all procedures are missing
- global variables needs to be cleaned
- temporary files needs to be cleaned
- temporary file names need to be unique (think about multiple instances)
- pollution of global Top namespace must be solved
- u is not a good name for a procedure

Library:
  finitediff.lib
Purpose:
  procedures to compute finite difference schemes for linear differential equations
Author:
  Christian Dingler

Overview:
  Using `qepcad`/`qepcadsystem` from this library requires the program `qepcad` to be installed. You can download `qepcad` from http://www.usna.edu/CS/qepcadweb/B/QEPCAD.html

Procedures:

> D.15.6.1 visualize |  | shows a scheme in index-notation
> D.15.6.2 u |  | gives some vector; depends on @derivatives
> D.15.6.3 scheme |  | computes the finite difference scheme defined by v1,..,vn
> D.15.6.4 laxfrT |  | Lax-Friedrich-approximation for the time-direction
> D.15.6.5 laxfrX |  | Lax-Friedrich-approximation for the space-direction
> D.15.6.6 forward |  | forward-approximation
> D.15.6.7 backward |  | backward-approximation
> D.15.6.8 central1st |  | central-approximation of first order
> D.15.6.9 central2nd |  | central-approximation of second order
> D.15.6.10 trapezoid |  | trapezoid-approximation
> D.15.6.11 midpoint |  | midpoint-approximation
> D.15.6.12 pyramid |  | pyramid-approximation
> D.15.6.13 setinitials |  | constructs and sets the basering for further computations
> D.15.6.14 errormap |  | performs the Fouriertransformation of a poly
> D.15.6.15 matrixsystem |  | gives the scheme of a pde-system as one matrix
> D.15.6.16 timestep |  | gives the several timelevels of a scheme derived from a pde-system
> D.15.6.17 fouriersystem |  | performs the Fouriertransformation of a matrix scheme
> D.15.6.18 PartitionVar |  | partitions a poly into the var(n)-part and the rest
> D.15.6.19 ComplexValue |  | computes the complex value of f, var(1) being the imaginary unit
> D.15.6.20 VarToPar |  | substitute var(i) by par(i)
> D.15.6.21 ParToVar |  | substitute par(i) by var(i)
> D.15.6.22 qepcad |  | ask QEPCAD for equivalent constraints to f<1
> D.15.6.23 qepcadsystem |  | ask QEPCAD for equivalent constraints to all eigenvals of some matrices being <1

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