Error analysis of the Tau method: Dependence of the approximation error on the choice of perturbation term.

*(English)*Zbl 0769.65045From 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.

An application of the results to the analysis of singularly perturbed differential equations is discussed.

Reviewer: C.Simerská (Praha)

##### MSC:

65L05 | Numerical methods for initial value problems |

34A34 | Nonlinear ordinary differential equations and systems, general theory |

##### Keywords:

perturbation; system of ordinary differential equations; constant coefficients; Tau method; error estimates; weighted residuals
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\textit{S. Namasivayam} and \textit{E. L. Ortiz}, Comput. Math. Appl. 25, No. 1, 89--104 (1993; Zbl 0769.65045)

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##### References:

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