Approximating semigroups by using pseudospectra

E. B. Davies

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Approximating semigroups by using pseudospectra

E. B. Davies

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Abstract

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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BibTeX RIS

E. B. Davies. 2003-03-19. Approximating semigroups by using pseudospectra. https://arxiv.org/abs/math/0303235

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