An application of Orthonormal Bernoulli polynomials for solving Generalized Abel’s integral equations

Authors

  • Nouradin Parandin Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
  • Ali Seifi Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
  • Mohsen Darabi Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Keywords:

Operational matrix method, Generalized Abel’s integral equation, Bernoulli polynomial

Abstract

Integral equations and specifically Generalized Abel’s integral equations (GAIEs), have been used to model3 various phenomena in applied science. In order to solve GAIEs, several numerical methods have been introduced4 in which they need a huge computation to converge. In this paper we developed a stable approach to solve5 GAIEs using Bernoulli’s orthogonal polynomials given by Gram-Schmidt orthogonalization algorithm. Since we6 did not employ the collocation points, we were able to decrease time computation considerably. In addition,7 several advantages of the proposed method were compared to previous works in the accuracy and performance.8 Also, under a few conditions, error bound and convergence analysis for the proposed method are established.9 Finally, several examples were provided to assess the suggested method. Results showed that our method had10 averagely an absolute error lower than other methods.

Published

2025-08-25

Issue

Vol. 19

Section

Vol. 19, No. 4, (2025)

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