Pseudospectra of a Spectral Approximation of the First Derivative
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
half-planes. This is suggested in this low-dimensional 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
[D,x] = cheb(18); % cheb.m from Trefethen's "Spectral Methods in MATLAB"
A = D(2:end,2:end);
opts.ax = [-60 10 -35 35];
opts.levels = -6:0;
Download this code: specdiff.m.
Download cheb.m from L. N. Trefethen,
Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.