The Tau Method

Previous article Next article The Tau MethodEduardo L. OrtizEduardo L. Ortizhttps://doi.org/10.1137/0706044PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1A] N. Bourbaki, Éléments de mathématique. Fasc. XX. Livre I: Théorie des ensembles. Chapitre 3: Ensembles ordonnés cardinaux, nombres entiers, Seconde édition, revue et augmentée. Actualités Sci. Indust., No. 1243, Hermann, Paris, 1963, 149– MR0154814 0125.00603 Google Scholar[1B] N. Bourbaki, Éléments de mathématique. Première partie. Fascicule VI. Livre II: Algèbre. Chapitre 2: Algèbre linéaire, Troisième édition, entièrement refondue, Actualités Sci. Indust., No. 1236. Hermann, Paris, 1962, 315– MR0155831 0142.00102 Google Scholar[2] T. Chaves and , E. L. Ortiz, On the numerical solution of two-point boundary value problems for linear differential equations, Z. Angew. Math. Mech., 48 (1968), 415–418 MR0246520 0172.19601 CrossrefISIGoogle Scholar[3] E. 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Ortiz , The solution of numerical problems in an automatic computer with the tau method , to appear Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A new Tau-collocation method with fractional basis for solving weakly singular delay Volterra integro-differential equationsJournal of Applied Mathematics and Computing, Vol. 68, No. 4 | 9 September 2021 Cross Ref A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systemsFractional Calculus and Applied Analysis, Vol. 25, No. 4 | 2 August 2022 Cross Ref On the convergence analysis of the Tau method applied to fourth-order partial differential equation based on Volterra-Fredholm integral equationsApplied Numerical Mathematics, Vol. 173 | 1 Mar 2022 Cross Ref Analysis of linear proportional delay systems via hybrid functions methodAsian Journal of Control, Vol. 24, No. 1 | 2 September 2020 Cross Ref Study of fourth-order boundary value problem based on Volterra–Fredholm equation: numerical treatmentInverse Problems in Science and Engineering, Vol. 29, No. 13 | 22 July 2021 Cross Ref Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral MethodsMathematical and Computational Applications, Vol. 26, No. 2 | 26 May 2021 Cross Ref Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic FoundationSymmetry, Vol. 12, No. 6 | 9 June 2020 Cross Ref Tau approximate solution of linear pantograph Volterra delay-integro-differential equationComputational and Applied Mathematics, Vol. 39, No. 2 | 7 February 2020 Cross Ref A Tau–like numerical method for solving fractional delay integro–differential equationsApplied Numerical Mathematics, Vol. 151 | 1 May 2020 Cross Ref Predicting critical ignition in slow-fast excitable modelsPhysical Review E, Vol. 101, No. 4 | 1 April 2020 Cross Ref Approximating the solution of integro-differential problems via the spectral Tau method with filteringApplied Numerical Mathematics, Vol. 149 | 1 Mar 2020 Cross Ref New fractional Lanczos vector polynomials and their application to system of Abel–Volterra integral equations and fractional differential equationsJournal of Computational and Applied Mathematics, Vol. 366 | 1 Mar 2020 Cross Ref A new recursive formulation of the Tau method for solving linear Abel–Volterra integral equations and its application to fractional differential equationsCalcolo, Vol. 56, No. 4 | 9 November 2019 Cross Ref An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution typeIMA Journal of Numerical Analysis, Vol. 39, No. 4 | 17 July 2018 Cross Ref Optimal residuals and the Dahlquist test problemNumerical Algorithms, Vol. 81, No. 4 | 20 November 2018 Cross Ref Unsteady Flow of Power Law Fluids With Wall Slip in MicroductsJournal of Fluids Engineering, Vol. 141, No. 8 | 19 February 2019 Cross Ref Tensor calculus in spherical coordinates using Jacobi polynomials. 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