Mathematics in Computer Science

, Volume 12, Issue 2, pp 197–205 | Cite as

Solving Differential and Integral Equations with Tau Method

  • J. C. Matos
  • J. M. A. Matos
  • M. J. Rodrigues


In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to compute the operational matrices. We also give numerical applications of operational matrices to solve differential and integral problems using the operational Tau method.


Operational Tau method Orthogonal polynomials Differential equations Integral equations 

Mathematics Subject Classification

80M22 45A05 


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  1. 1.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions, 9th edn. Dover Publications, New York (1972)zbMATHGoogle Scholar
  2. 2.
    Canuto, C., Hussaini, M., Quarteroni, A., Zang, T.: Spectral Methods. Scientific Computation, Fundamentals in Single Domains. Springer, Berlin (2006)zbMATHGoogle Scholar
  3. 3.
    Funaro, D.: Polynomial Approximations of Differential Equations. Springer, Berlin (1992)zbMATHGoogle Scholar
  4. 4.
    Gottlieb, D., Orszag, S.: Numerical Analysis of Spectral Methods: Theory and Applications. SIAM-CBMS, Philadelphia (1977)CrossRefzbMATHGoogle Scholar
  5. 5.
    Ortiz, E.L., Samara, H.: A new operational approach to the numerical solution of differential equations in terms of polynomials. In: Shaw, R., Pilkey, W. (eds.) Innovative Numerical Analysis for the Engineering Sciences, pp. 643–652. The University Press of Virginia, Charlottesville (1980)Google Scholar
  6. 6.
    Ortiz, E.L., Samara, H.: An operational approach to the tau method for the numerical solution of non-linear differential equations. Computing 27(1), 15–25 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Matos, J.M.A., Rodrigues, M.J., Matos, J.C.: Explicit formulae for derivatives and primitives of orthogonal polynomials (2017). arXiv:1703.00743v2 [math.NA]

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • J. C. Matos
    • 1
  • J. M. A. Matos
    • 1
  • M. J. Rodrigues
    • 2
  1. 1.Instituto Superior de Engenharia do PortoPortoPortugal
  2. 2.Faculdade of Ciências da Universidade do PortoPortoPortugal

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