Pseudospectra of a Spectral Approximation of the Convection-Diffusion Operator
This figure illustrates approximate pseudospectra of the 1-D convection-diffusion
operator u'' + u' on L2[0,d] with
u(0)=u(d)=0 for d=80.
The boundaries of pseudospectra of
the infinite dimensional operator are shaped approximately like parabolas,
as already revealed on the right part of this low-dimensional approximation.
For more information, see
Use the following MATLAB code compute a similar image using
[D,x] = cheb(40); % cheb.m from Trefethen's "Spectral Methods in MATLAB"
A = D^2/1600 + D/40;
A = A(2:end-1,2:end-1);
opts.ax = [-3.75 0.25 -1.25 1.25];
opts.levels = -10:-1;
Download this code: convdiff.m.
Download cheb.m from L. N. Trefethen,
Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.