Fourdif.m

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Fourier spectral differentiation matrices.

Syntax

    [x,DM]=fourdif(N,m)

Description

Computes the m'th derivative Fourier spectral differentiation matrix on grid with N equispaced points in [0,2pi).

Arguments

    N -       size of differentiation matrix

    m -       derivative order

Outputs

    x -       equispaced points 0, 2pi/N, 4pi/N, ... , (N-1)2pi/N

   DM -       m-th order differentiation matrix

Notes

Explicit formulas are used to compute the matrices for m=1 and m=2. A discrete Fourier approach is employed for m>2. The program computes the first column and first row and then uses the toeplitz command to create the matrix.

For m=1 and 2 the code implements a "flipping trick" to improve accuracy suggested in http://dx.doi.org/10.1137/0916073

See also

fdmat.m, fdvec.m, v2fplanck.m, hydrodynamics.m, fourlap.m


Version 2.1, authors: S.C. Reddy, J.A.C. Weideman