fourdif.m

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

Syntax

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

Parameters

    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, acomm.m, arnoldi.m, atranspose.m, aux_mat.m, binpack.m, cheap_norm.m, cheb_coeff.m, clean_up.m, dirdiff.m, eigenfields.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, frob_chop.m, gaussfun.m, hdot.m, herm_spline.m, jacobianest.m, keep_rank.m, krondelta.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, remncomm.m, remtrace.m, rspert.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, tikhonov.m, trapdiff.m, unit_oper.m, unit_state.m, vvpert.m, Kernel_utilities

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