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A convergence result for the Tau method

Eine Konvergenzaussage für die Tau-Methode

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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.


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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  1. [1]

    Ortiz, E. L., Samara, H.: An operational approach to the tau method for the numerical solution of nonlinear differential equations. Computing27, 15–25 (1981).

  2. [2]

    Vainikko, G.: Funktionalanalyse der Diskretisierungsmethoden. Leizig: Teubner-Verlagsgesellschaft 1976.

  3. [3]

    Krasnosiels'kii, M. A., et al.: Approximate Solution of Operator Equations. Groningen: Wolters-Noordhoff Publishing 1972.

  4. [4]

    Roos, H.-G., Pfeifer, E.: Die Tau-Methode. Preprint 07-08-88, TU Dresden, p. 22.

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Roos, H.-., Pfeifer, E. A convergence result for the Tau method. Computing 42, 81–84 (1989). https://doi.org/10.1007/BF02243145

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AMS Subject Classification

  • 65L

Key words

  • Tau method
  • Galerkin-Petrov method