Approximating semigroups by using pseudospectra

Details Approximating semigroups by using pseudospectra Approximating semigroups by using pseudospectra

2003-03-19

arxiv.org/abs/math/0303235v1

Mathematics

Spectral Theory

22 pages, 2 figures

Scientific paper

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.

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