2003/03/19 by E. B. Davies, Davies, E. B.
Mathematics · #35Pxx #42C99 #47Dxx #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35Pxx #msc:42C99 #msc:47Dxx
paper · pdf · doi:10.48550/arxiv.math/0303235
22 pages, 2 figures
arxiv created 2003/03/19 · arxiv updated 2009/11/30
We study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equations, because they are so ill-conditioned. We introduce a new method using pseusospectra to produce an approximated spectral expansion, and explain its theoretical status. We also give some simple numerical examples to show that it is much better conditioned.