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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.
@article{M2AN_2007__41_6_1021_0,
author = {Fatone, Lorella and Funaro, Daniele and Scannavini, Valentina},
title = {Finite-difference preconditioners for superconsistent pseudospectral approximations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1021--1039},
publisher = {EDP-Sciences},
volume = {41},
number = {6},
year = {2007},
doi = {10.1051/m2an:2007052},
mrnumber = {2377105},
zbl = {1133.65103},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007052/}
}
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 PY - 2007 SP - 1021 EP - 1039 VL - 41 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007052/ DO - 10.1051/m2an:2007052 LA - en ID - M2AN_2007__41_6_1021_0 ER -
%0 Journal Article %A Fatone, Lorella %A Funaro, Daniele %A Scannavini, Valentina %T Finite-difference preconditioners for superconsistent pseudospectral approximations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2007 %P 1021-1039 %V 41 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007052/ %R 10.1051/m2an:2007052 %G en %F M2AN_2007__41_6_1021_0
Fatone, Lorella; Funaro, Daniele; Scannavini, Valentina. Finite-difference preconditioners for superconsistent pseudospectral approximations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 6, pp. 1021-1039. doi: 10.1051/m2an:2007052
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