Finite-difference preconditioners for superconsistent pseudospectral approximations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, p. 1021-1039

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.

DOI : https://doi.org/10.1051/m2an:2007052
Classification:  65N35,  65F15,  41A10
Keywords: spectral collocation method, preconditioning, superconsistency, Lebesgue constant
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {6},
     year = {2007},
     pages = {1021-1039},
     doi = {10.1051/m2an:2007052},
     zbl = {1133.65103},
     mrnumber = {2377105},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, pp. 1021-1039. doi : 10.1051/m2an:2007052. http://www.numdam.org/item/M2AN_2007__41_6_1021_0/

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