Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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FAMILIES OF NONLINEAR TRANSFORMATIONS FOR ACCURATE EVALUATION OF WEAKLY SINGULAR INTEGRALS

  • BEONG IN YUN (DEPARTMENT OF MATHEMATICS, KUNSAN NATIONAL UNIVERSITY)
  • Received : 2023.06.20
  • Accepted : 2023.09.23
  • Published : 2023.09.25
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Abstract

We present families of nonlinear transformations useful for numerical evaluation of weakly singular integrals. First, for end-point singular integrals, we define a prototype function with some appropriate features and then suggest a family of transformations. In addition, for interior-point singular integrals, we develop a family of nonlinear transformations based on the aforementioned prototype function. We take some examples to explore the efficiency of the proposed nonlinear transformations in using the Gauss-Legendre quadrature rule. From the numerical results, we can find the superiority of the proposed transformations compared to some existing transformations, especially for the integrals with high singularity strength.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) [No. 2021R1F1A1047343].

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