Finite-difference preconditioners for superconsistent pseudospectral approximations

Lorella Fatone; Daniele Funaro; Valentina Scannavini

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 6, page 1021-1039
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Fatone, Lorella, Funaro, Daniele, and Scannavini, Valentina. "Finite-difference preconditioners for superconsistent pseudospectral approximations." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1021-1039. <http://eudml.org/doc/250039>.

@article{Fatone2007,
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. },
author = {Fatone, Lorella, Funaro, Daniele, Scannavini, Valentina},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Spectral collocation method; preconditioning; superconsistency; Lebesgue constant.; spectral collocation; superconsistency; Lebesgue constant; numerical results; finite differences; advection-diffusion boundary value problems},
language = {eng},
month = {12},
number = {6},
pages = {1021-1039},
publisher = {EDP Sciences},
title = {Finite-difference preconditioners for superconsistent pseudospectral approximations},
url = {http://eudml.org/doc/250039},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Fatone, Lorella
AU - Funaro, Daniele
AU - Scannavini, Valentina
TI - Finite-difference preconditioners for superconsistent pseudospectral approximations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/12//
PB - EDP Sciences
VL - 41
IS - 6
SP - 1021
EP - 1039
AB - 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.
LA - eng
KW - Spectral collocation method; preconditioning; superconsistency; Lebesgue constant.; spectral collocation; superconsistency; Lebesgue constant; numerical results; finite differences; advection-diffusion boundary value problems
UR - http://eudml.org/doc/250039
ER -

References

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