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

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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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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Keywords

  • 2D integral equations
  • Non-rectangular domains
  • Collocation method
  • Jacobi polynomials