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Finite-difference preconditioners for superconsistent pseudospectral approximations

Published online by Cambridge University Press:  15 December 2007

Lorella Fatone ,
Daniele Funaro  and
Valentina Scannavini
Lorella Fatone
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b, Università di Modena e Reggio Emilia, Modena 41110, Italy. lorella.fatone@unimo.it; daniele.funaro@unimo.it; s.valentina@tin.it
Daniele Funaro
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b, Università di Modena e Reggio Emilia, Modena 41110, Italy. lorella.fatone@unimo.it; daniele.funaro@unimo.it; s.valentina@tin.it
Valentina Scannavini
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b, Università di Modena e Reggio Emilia, Modena 41110, Italy. lorella.fatone@unimo.it; daniele.funaro@unimo.it; s.valentina@tin.it
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Abstract

The superconsistent collocation method, which is based on acollocation grid different from the one used to represent thesolution, has proven to be very accurate in the resolution ofvarious functional equations. Excellent results can be alsoobtained for what concerns preconditioning. Some analysis andnumerous experiments, regarding the use of finite-differencespreconditioners, for matrices arising from pseudospectralapproximations of advection-diffusion boundary value problems, arepresented and discussed, both in the case of Legendre andChebyshev representation nodes.

Keywords

Spectral collocation methodpreconditioningsuperconsistencyLebesgue constant.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 6 , November 2007 , pp. 1021 - 1039
Copyright
© EDP Sciences, SMAI, 2007

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