A convergence result for the Tau method (Q1123564)

The authors show that the operational approach to the Tau method of \textit{E. L. Ortiz} and \textit{H. Samara} [ibid. 27, 15-25 (1981; Zbl 0449.65053)] turns out, in the most interesting cases, to a method of Galerkin-Petrov method. Thus, under the framework of the orthogonalized polynomial base with some weight function, the convergence of the Tau method follows from convergence theorems presented by \textit{G. Vainikho} [Funktionalanalysis der Diskretisierungsmethoden (1976; Zbl 0343.65023)].