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superconsistency

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Finite-difference preconditioners for superconsistent pseudospectral approximations
Lorella Fatone, Daniele Funaro, Valentina Scannavini
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 6 / November 2007

Published online by Cambridge University Press:

15 December 2007, pp. 1021-1039

Print publication:

November 2007
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The superconsistent collocation method, which is based on acollocation grid different from the one used to represent thesolution, has proven to be very accurate in the resolution ofvarious functional equations. Excellent results can be alsoobtained for what concerns preconditioning. Some analysis andnumerous experiments, regarding the use of finite-differencespreconditioners, for matrices arising from pseudospectralapproximations of advection-diffusion boundary value problems, arepresented and discussed, both in the case of Legendre andChebyshev representation nodes.