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Solving two-dimensional integral equations of the second kind on non-rectangular domains with error estimate

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Abstract

In this paper, the collocation method is applied on two-dimensional integral equations of the second kind on non-rectangular domains. Since the domains of these equations are non-rectangular and so directly applying the collocation method for them is difficult, at first, the integral equations are converted to equivalent integral equations on rectangular domains. Then, two-dimensional Jacobi collocation method is applied. Furthermore, an error estimate for the method is investigated and several examples demonstrate the accuracy and efficiency of the method.

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Authors and Affiliations

  1. Department of Computer Sciences, Shahid Beheshti University, Tehran, Iran

    Kourosh Parand & Hafez Yari

  2. Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran

    Kourosh Parand

  3. Department of Mathematics and Computer Sciences, Islamic Azad University, Bardaskan Branch, Bardaskan, Iran

    Mehdi Delkhosh

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  1. Kourosh Parand
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  2. Hafez Yari
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  3. Mehdi Delkhosh
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Correspondence to Kourosh Parand.

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Parand, K., Yari, H. & Delkhosh, M. Solving two-dimensional integral equations of the second kind on non-rectangular domains with error estimate. Engineering with Computers 36, 725–739 (2020). https://doi.org/10.1007/s00366-019-00727-y

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