A Convergence Result For The Tau Method

Roos, Hans–Görg; Pfeifer, E.

doi:10.1515/dema-1990-0413

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2016

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“…The recursive form of the Tau method, formalized by Ortiz in [20], was extended to the case of systems of ordinary differential equations in [35], and also an error analysis was given there. In [36] Roos and Pfeifer showed that the Tau method is, in the most interesting cases, a method of Galerkin-Petrov type, thus the convergence of the method follows from Vainikko's convergence theorem [37].…”

Section: Introductionmentioning

confidence: 99%

Segmented Tau Approximation for a Non-Autonomous Functional Differential Equation of Mixed Type

Silva¹,

Escalante²

2016

Preprint

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The segmented formulation of the Tau method is used to numerically solve the non-autonomous forward-backward functional differential equationwhere x is the unknown function, a, b, and c are known functions. The step by step Tau method is applied to approximate the solution of this equation by a piecewise polynomial function. A boundary value problem is posed, numerically solved, and analyzed. Also, a novel way to generate a set of non-autonomous problems with known analytical solution is provided. From it, several nonautonomous problems were constructed and resolved with the proposed method. We conclude that the good numerical results obtained in our numerical experimentation and the relative simplicity of the Tau method demonstrate that it is a promising strategy for numerically solving mixed-type problems, as presented here.

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Section: Introductionmentioning

confidence: 99%