A convergence result for the Tau method
Copyright policy )A convergence result for the Tau method
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)].
Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, polynomial coefficients, Galerkin-Petrov method, Numerical solutions to equations with linear operators, ordinary linear differential operator, Linear boundary value problems for ordinary differential equations, Tau method, Equations and inequalities involving linear operators, with vector unknowns
Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, polynomial coefficients, Galerkin-Petrov method, Numerical solutions to equations with linear operators, ordinary linear differential operator, Linear boundary value problems for ordinary differential equations, Tau method, Equations and inequalities involving linear operators, with vector unknowns
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