Pseudospectra of a Spectral Approximation of the First Derivative
Dimension N=17
This figure illustrates approximate pseudospectra of the first derivative operator
d/dx on [1,1] with boundary condition u(1)=0.
The pseudospectra of the infinite dimensional operator consist of
halfplanes. This is suggested in this lowdimensional discretization
by the straight lines that form the rightmost part of each pseudospectral
boundary. For more information, see [Tre92].
Use the following MATLAB code compute a similar image using
EigTool.
[D,x] = cheb(18); % cheb.m from Trefethen's "Spectral Methods in MATLAB"
A = D(2:end,2:end);
opts.npts=50;
opts.ax = [60 10 35 35];
opts.levels = 6:0;
eigtool(A,opts)
Download this code: specdiff.m.
Download cheb.m from L. N. Trefethen,
Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.
