Pseudospectra of a Spectral Approximation of the ConvectionDiffusion Operator
Dimension N=39
This figure illustrates approximate pseudospectra of the 1D convectiondiffusion
operator u'' + u' on L^{2}[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 lowdimensional approximation.
For more information, see
[RT94].
Use the following MATLAB code compute a similar image using
EigTool.
[D,x] = cheb(40); % cheb.m from Trefethen's "Spectral Methods in MATLAB"
A = D^2/1600 + D/40;
A = A(2:end1,2:end1);
opts.npts=50;
opts.ax = [3.75 0.25 1.25 1.25];
opts.levels = 10:1;
eigtool(A,opts)
Download this code: convdiff.m.
Download cheb.m from L. N. Trefethen,
Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.
