D.15.4 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.15.4.1 visualize		shows a scheme in index-notation
D.15.4.2 u		gives some vector; depends on @derivatives
D.15.4.3 scheme		computes the finite difference scheme defined by v1,..,vn
D.15.4.4 laxfrT		Lax-Friedrich-approximation for the time-direction
D.15.4.5 laxfrX		Lax-Friedrich-approximation for the space-direction
D.15.4.6 forward		forward-approximation
D.15.4.7 backward		backward-approximation
D.15.4.8 central1st		central-approximation of first order
D.15.4.9 central2nd		central-approximation of second order
D.15.4.10 trapezoid		trapezoid-approximation
D.15.4.11 midpoint		midpoint-approximation
D.15.4.12 pyramid		pyramid-approximation
D.15.4.13 setinitials		constructs and sets the basering for further computations
D.15.4.14 errormap		performs the Fouriertransformation of a poly
D.15.4.15 matrixsystem		gives the scheme of a pde-system as one matrix
D.15.4.16 timestep		gives the several timelevels of a scheme derived from a pde-system
D.15.4.17 fouriersystem		performs the Fouriertransformation of a matrix scheme
D.15.4.18 PartitionVar		partitions a poly into the var(n)-part and the rest
D.15.4.19 ComplexValue		computes the complex value of f, var(1) being the imaginary unit
D.15.4.20 VarToPar		substitute var(i) by par(i)
D.15.4.21 ParToVar		substitute par(i) by var(i)
D.15.4.22 qepcad		ask QEPCAD for equivalent constraints to f<1
D.15.4.23 qepcadsystem		ask QEPCAD for equivalent constraints to all eigenvals of some matrices being <1