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A Time-Splitting Tau Method for PDE’s: A Contribution for the Spectral Tau Toolbox Library

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Abstract

This paper presents implementation details of an extension of the algebraic formulation for the spectral Tau method for the numerical solution of time-space partial differential problems, together with illustrative numerical examples. This extension implementation highlights (i) the orthogonal basis choice, (ii) the construction of the problem’s algebraic representation and (iii) the mechanisms to tackle certain partial differential problems with ease. This effort will be delivered to the scientific community as a crucial building block of the Tau Toolbox (a numerical library for the solution of integro-differential problems).

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Authors and Affiliations

  1. Faculty of Sciences, and CMUP, University of Porto, Rua Campo Alegre s/n, 4169-007, Porto, Portugal

    N. Lima

  2. Faculty of Economics and Business, and CMUP, University of Porto, Rua Dr. Roberto Frias s/n, 4200-464, Porto, Portugal

    J. A. O. Matos

  3. School of Engineering, and CMUP, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. M. A. Matos

  4. Faculty of Economics and Business, CMUP and CEF.UP, University of Porto, Rua Dr. Roberto Frias s/n, 4200-464, Porto, Portugal

    P. B. Vasconcelos

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  1. N. Lima
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  2. J. A. O. Matos
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  3. J. M. A. Matos
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  4. P. B. Vasconcelos
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Correspondence to P. B. Vasconcelos.

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This research has been financed by Portuguese public funds through FCT - Fundação para a Ciência e a Tecnologia, I.P., in the framework of the project with reference UIDB/00144/2020.

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Lima, N., Matos, J.A.O., Matos, J.M.A. et al. A Time-Splitting Tau Method for PDE’s: A Contribution for the Spectral Tau Toolbox Library. Math.Comput.Sci. 16, 7 (2022). https://doi.org/10.1007/s11786-022-00526-7

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  • DOI: https://doi.org/10.1007/s11786-022-00526-7

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