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The tau method and a new preconditioner. (English) Zbl 1046.65060
The authors present a formulation of the tau method that makes use of fact that the derivatives of the Chebyshev and Legendre polynomials are Gegenbauer polynomials of higher index. This allows them to find suitable preconditioners. Numerical results are included.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65F35 Numerical computation of matrix norms, conditioning, scaling
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