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Finite-difference preconditioners for superconsistent pseudospectral approximations. (English) Zbl 1133.65103
The superconsistent collocation method has proven to be very accurate in the resolution of various functional equations. Excellent results are also obtained with respect to preconditioning. Some analysis and numerical results are presented for the preconditioning with finite differences, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems. The results are obtained both for Legendre and Chebyshev representation nodes.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F35 Numerical computation of matrix norms, conditioning, scaling
65N06 Finite difference methods for boundary value problems involving PDEs
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