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

Document Type : Regular paper


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

2 Imam Khomeini Int. University, Qazvin, Iran.


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.


Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 27-34
  • Receive Date: 18 October 2022
  • Accept Date: 02 December 2022
  • First Publish Date: 02 December 2022