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D.15.15 finitediff_lib


  • 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

procedures to compute finite difference schemes for linear differential equations
Christian Dingler

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


D.15.15.1 visualize  shows a scheme in index-notation
D.15.15.2 u  gives some vector; depends on @derivatives
D.15.15.3 scheme  computes the finite difference scheme defined by v1,..,vn
D.15.15.4 laxfrT  Lax-Friedrich-approximation for the time-direction
D.15.15.5 laxfrX  Lax-Friedrich-approximation for the space-direction
D.15.15.6 forward  forward-approximation
D.15.15.7 backward  backward-approximation
D.15.15.8 central1st  central-approximation of first order
D.15.15.9 central2nd  central-approximation of second order
D.15.15.10 trapezoid  trapezoid-approximation
D.15.15.11 midpoint  midpoint-approximation
D.15.15.12 pyramid  pyramid-approximation
D.15.15.13 setinitials  constructs and sets the basering for further computations
D.15.15.14 errormap  performs the Fouriertransformation of a poly
D.15.15.15 matrixsystem  gives the scheme of a pde-system as one matrix
D.15.15.16 timestep  gives the several timelevels of a scheme derived from a pde-system
D.15.15.17 fouriersystem  performs the Fouriertransformation of a matrix scheme
D.15.15.18 PartitionVar  partitions a poly into the var(n)-part and the rest
D.15.15.19 ComplexValue  computes the complex value of f, var(1) being the imaginary unit
D.15.15.20 VarToPar  substitute var(i) by par(i)
D.15.15.21 ParToVar  substitute par(i) by var(i)
D.15.15.22 qepcad  ask QEPCAD for equivalent constraints to f<1
D.15.15.23 qepcadsystem  ask QEPCAD for equivalent constraints to all eigenvals of some matrices being <1