Abstract
An operational formulation of the Tau method, based on a reduced set of matrix operations, is presented in this paper. It is applicable to the numerical solution of linear and nonlinear initial value, boundary value, and mixed problems for ordinary differential equations. It provides a convenient framework for the implementation of the Tau method and related polynomial methods, such as collocation and Chebyshev or Legendre series replacement.
Zusammenfassung
In der Arbeit wird eine operationelle Formulierung der Tau-Methode vorgestellt, die auf einem reduzierten Satz von Matrix-Operationen aufbaut. Sie läßt sich auf die numerische Lösung von linearen und nichtlinearen Anfangswert-, Randwert- und gemischten Problemen für gewöhnliche Differentialgleichungen anwenden. Sie bildet einen geeigneten Hintergrund für die Implementierung der Tau-Methode und verwandter Polynom-Methoden, wie Kollokation und Chebyshev- oder Legendre-Reihen.
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Ortiz, E.L., Samara, H. An operational approach to the Tau method for the numerical solution of non-linear differential equations. Computing 27, 15–25 (1981). https://doi.org/10.1007/BF02243435
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DOI: https://doi.org/10.1007/BF02243435