Difference between revisions of "Fdmat.m"
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| − | Returns arbitrary-order central finite-difference differentiation | + | {{DISPLAYTITLE:fdmat.m}} __NOTOC__ |
| + | Returns arbitrary-order central finite-difference differentiation matrices (sparse) with unit grid point spacing. | ||
| − | + | ==Syntax== | |
| − | Parameters | + | D=fdmat(dim,nstenc,order,boundary) |
| + | |||
| + | ==Parameters== | ||
dim - dimension of the column vector to be | dim - dimension of the column vector to be | ||
differentiated | differentiated | ||
| − | + | ||
| − | + | nstenc - number of points in the finite diffe- | |
rence stencil | rence stencil | ||
| − | + | ||
order - order of the derivative required | order - order of the derivative required | ||
| − | + | ||
boundary - 'wall' fills the edges with sided | boundary - 'wall' fills the edges with sided | ||
finite difference schemes, 'pbc' | finite difference schemes, 'pbc' | ||
assumes periodic boundaries. The | assumes periodic boundaries. The | ||
| − | default is ' | + | default is 'pbc'. |
| + | |||
| + | ==Outputs== | ||
| + | |||
| + | D - finite difference differentiation matrix | ||
| + | |||
| + | ==Examples== | ||
| + | A three-point second derivative matrix designed to act on a vector with ten elements with periodic boundary conditions is: | ||
| + | |||
| + | >> full(fdmat(10,3,2,'pbc')) | ||
| + | |||
| + | ans = | ||
| + | |||
| + | -2 1 0 0 0 0 0 0 0 1 | ||
| + | 1 -2 1 0 0 0 0 0 0 0 | ||
| + | 0 1 -2 1 0 0 0 0 0 0 | ||
| + | 0 0 1 -2 1 0 0 0 0 0 | ||
| + | 0 0 0 1 -2 1 0 0 0 0 | ||
| + | 0 0 0 0 1 -2 1 0 0 0 | ||
| + | 0 0 0 0 0 1 -2 1 0 0 | ||
| + | 0 0 0 0 0 0 1 -2 1 0 | ||
| + | 0 0 0 0 0 0 0 1 -2 1 | ||
| + | 1 0 0 0 0 0 0 0 1 -2 | ||
| + | |||
| + | ==See also== | ||
| + | [[fdvec.m]], [[fdlap.m]], [[fdhess.m]], [[fdkup.m]], [[fdweights.m]], [[fftdiff.m]], [[fourdif.m]], [[fourlap.m]], [[cgsppm2ang.m]], [[corrfun.m]], [[fpl2phan.m]], [[fpl2rho.m]], [[hydrodynamics.m]], [[interpmat.m]], [[oscillator.m]], [[overwound.m]], [[phan2fpl.m]], [[points2mult.m]], [[qform2sph.m]], [[qxspen_kernel.m]], [[spden.m]], [[Hyperfine_shift_module]], [[Kernel_utilities]] | ||
| + | |||
| + | ''Version 2.2, authors: [[Ilya Kuprov]]'' | ||
Latest revision as of 19:36, 6 June 2026
Returns arbitrary-order central finite-difference differentiation matrices (sparse) with unit grid point spacing.
Syntax
D=fdmat(dim,nstenc,order,boundary)
Parameters
dim - dimension of the column vector to be
differentiated
nstenc - number of points in the finite diffe-
rence stencil
order - order of the derivative required
boundary - 'wall' fills the edges with sided
finite difference schemes, 'pbc'
assumes periodic boundaries. The
default is 'pbc'.
Outputs
D - finite difference differentiation matrix
Examples
A three-point second derivative matrix designed to act on a vector with ten elements with periodic boundary conditions is:
>> full(fdmat(10,3,2,'pbc'))
ans =
-2 1 0 0 0 0 0 0 0 1
1 -2 1 0 0 0 0 0 0 0
0 1 -2 1 0 0 0 0 0 0
0 0 1 -2 1 0 0 0 0 0
0 0 0 1 -2 1 0 0 0 0
0 0 0 0 1 -2 1 0 0 0
0 0 0 0 0 1 -2 1 0 0
0 0 0 0 0 0 1 -2 1 0
0 0 0 0 0 0 0 1 -2 1
1 0 0 0 0 0 0 0 1 -2
See also
fdvec.m, fdlap.m, fdhess.m, fdkup.m, fdweights.m, fftdiff.m, fourdif.m, fourlap.m, cgsppm2ang.m, corrfun.m, fpl2phan.m, fpl2rho.m, hydrodynamics.m, interpmat.m, oscillator.m, overwound.m, phan2fpl.m, points2mult.m, qform2sph.m, qxspen_kernel.m, spden.m, Hyperfine_shift_module, Kernel_utilities
Version 2.2, authors: Ilya Kuprov
