Abstract
We show that the operational approach to the Tau method of Ortiz and Samara is, in the most interesting cases, a method of Galerkin-Petrov type. The convergence of the method follows from Vainikko's convergence theorem.
Zusammenfassung
Wir zeigen, daß der Operatorenzugang zur Tau-Methode von Ortiz und Samara in den interessanten Anwendungsfällen mit einem Galerkin-Petrov-Verfahren zusammenfällt. Die Konvergenz der genannten Methode resultiert aus Konvergenzsätzen von Vainikko.
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Ortiz, E. L., Samara, H.: An operational approach to the tau method for the numerical solution of nonlinear differential equations. Computing27, 15–25 (1981).
Vainikko, G.: Funktionalanalyse der Diskretisierungsmethoden. Leizig: Teubner-Verlagsgesellschaft 1976.
Krasnosiels'kii, M. A., et al.: Approximate Solution of Operator Equations. Groningen: Wolters-Noordhoff Publishing 1972.
Roos, H.-G., Pfeifer, E.: Die Tau-Methode. Preprint 07-08-88, TU Dresden, p. 22.
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Roos, H.G., Pfeifer, E. A convergence result for the Tau method. Computing 42, 81–84 (1989). https://doi.org/10.1007/BF02243145
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DOI: https://doi.org/10.1007/BF02243145