Finite-difference preconditioners for superconsistent pseudospectral approximations
Dipartimento di Matematica Pura ed Applicata, via Campi 213/b,
Università di Modena e Reggio Emilia, Modena 41110, Italy.
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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.
Mathematics Subject Classification: 65N35 / 65F15 / 41A10
Key words: Spectral collocation method / preconditioning / superconsistency / Lebesgue constant.
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