Finite-difference preconditioners for superconsistent pseudospectral approximations

被引：1
|
作者：
Fatone, Lorella [1 ]
Funaro, Daniele [1 ]
Scannavini, Valentina [1 ]
机构：
[1] Univ Modena & Reggio Emilia, Dipartimento Matemat Pura & Applicata, I-41110 Modena, Italy
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2007年 / 41卷 / 06期
关键词：
spectral collocation method; preconditioning; superconsistency; Lebesgue constant;
D O I：
10.1051/m2an:2007052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：1021 / 1039
页数：19
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