Mathematics in Computer Science

, Volume 12, Issue 2, pp 183–195 | Cite as

Dealing with Functional Coefficients Within Tau Method

  • M. Trindade
  • J. Matos
  • P. B. VasconcelosEmail author


The spectral tau method was originally proposed by Lanczos for the solution of linear differential problems with polynomial coefficients. In this contribution we present three approaches to tackle integro-differential equations with non-polynomial coefficients: (i) making use of functions of matrices, (ii) applying orthogonal interpolation and (iii) solving auxiliary differential problems by the tau method itself. These approaches are part of the Tau Toolbox efforts for deploying a numerical library for the solution of integro-differential problems. Numerical experiments illustrate the use of all these polynomial approximations in the context of the tau method.


Spectral methods Initial and boundary value problems Software 

Mathematics Subject Classification

68N01 68N19 65L05 65L10 47G20 34K28 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of SciencesUniversity of PortoPortoPortugal
  2. 2.Laboratório Engenharia Matemática, Center of Mathematics, Instituto Superior Engenharia PortoUniversity of PortoPortoPortugal
  3. 3.Center of Mathematics, Faculty of EconomicsUniversity of PortoPortoPortugal

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