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Reproducing kernel method for Abel's second kind singular integral equations

    Authors

    • Nazi Abdollahi 1
    • Saeid Abbasbandy 2

    1 Civil Engineering Department, Miaad University, Mahabad, 59141-673635, Iran

    2 Imam Khomeini Int. University, Qazvin, Iran.

,

Document Type : Regular paper

10.52547/CMCMA.1.2.27
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Abstract

Singular integral equations (SIEs) are often encountered in certain contact and fracture problems in solid mechanics. In this paper, we apply the reproducing kernel method (RKM) to give the approximate solution of Abel's second-kind singular integral equations. For solving this problem, difficulties lie in its singular term. In order to remove the singular term of the equation, an equivalent transformation is made. Solution representations are obtained in reproducing kernel Hilbert space. Numerical experiments show that our reproducing kernel method is efficient. To show the high accuracy of the method the results are compared to other numerical methods and satisfactory agreements are achieved.

Keywords

  • Abel integral equation
  • Reproducing Hilbert kernel space
  • Approximate solution
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 27-34
Files
  • XML
  • PDF 367.95 K
History
  • Receive Date: 18 October 2022
  • Accept Date: 02 December 2022
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
  • VANCOUVER
Statistics
  • Article View: 149
  • PDF Download: 244

APA

Abdollahi, N. and Abbasbandy, S. (2022). Reproducing kernel method for Abel's second kind singular integral equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), 27-34. doi: 10.52547/CMCMA.1.2.27

MLA

Abdollahi, N. , and Abbasbandy, S. . "Reproducing kernel method for Abel's second kind singular integral equations", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 2, 2022, 27-34. doi: 10.52547/CMCMA.1.2.27

HARVARD

Abdollahi, N., Abbasbandy, S. (2022). 'Reproducing kernel method for Abel's second kind singular integral equations', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), pp. 27-34. doi: 10.52547/CMCMA.1.2.27

CHICAGO

N. Abdollahi and S. Abbasbandy, "Reproducing kernel method for Abel's second kind singular integral equations," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 2 (2022): 27-34, doi: 10.52547/CMCMA.1.2.27

VANCOUVER

Abdollahi, N., Abbasbandy, S. Reproducing kernel method for Abel's second kind singular integral equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(2): 27-34. doi: 10.52547/CMCMA.1.2.27

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