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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. [email protected]; [email protected]; [email protected]
Daniele Funaro
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b, Università di Modena e Reggio Emilia, Modena 41110, Italy. [email protected]; [email protected]; [email protected]
Valentina Scannavini
Affiliation:
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b, Università di Modena e Reggio Emilia, Modena 41110, Italy. [email protected]; [email protected]; [email protected]
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Abstract

The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented and discussed, both in the case of Legendre and Chebyshev 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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