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Computing some classes of Cauchy type singular integrals with Mathematica software

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Abstract

We constructed an algorithm, [SInt], for computing some classes of Cauchy type singular integrals on the unit circle. The design of [SInt] was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithm. Furthermore, we show how the factorization algorithm described in Conceição et al. (2010) allowed us to construct and implement the [SIntAFact] algorithm for calculating several interesting singular integrals that cannot be computed by [SInt]. All the above techniques were implemented using the symbolic computation capabilities of the computer algebra system Mathematica. The corresponding source code of [SInt] is made available in this paper. Several examples of nontrivial singular integrals computed with both algorithms are presented.

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Authors and Affiliations

  1. CEAF, CEDMES, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Ana C. Conceição & Viktor G. Kravchenko

  2. CEAF, CEDMES, Departamento de Engenharia Electrónica e Informática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    José C. Pereira

Authors
  1. Ana C. Conceição
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  2. Viktor G. Kravchenko
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  3. José C. Pereira
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Correspondence to Ana C. Conceição.

Additional information

Communicated by: Zhongying Chen.

This research was partially supported by CEAF at Instituto Superior Técnico (Portugal).

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Conceição, A.C., Kravchenko, V.G. & Pereira, J.C. Computing some classes of Cauchy type singular integrals with Mathematica software. Adv Comput Math 39, 273–288 (2013). https://doi.org/10.1007/s10444-012-9279-7

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  • DOI: https://doi.org/10.1007/s10444-012-9279-7

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