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Error analysis of the Tau method: Dependence of the approximation error on the choice of perturbation term. (English) Zbl 0769.65045
From the author’s abstract: A system of ordinary differential equations with constant coefficients and asymptotic estimates for the Tau method approximation error vector per step for different choices of the perturbation term \(H_ n(x)\) is considered. The resulting Tau method implementation can be arranged into the following scale of increasing error estimates at the end point: Legendre \(<\) Chebyshev \(\ll\) Power series \(<\) Weighted residuals.
An application of the results to the analysis of singularly perturbed differential equations is discussed.

MSC:
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
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