SOLVING FREDHOLM INTEGRAL EQUATIONS USING
BEES ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS
Azzam S.Y. Aladool1, Mohammed Abdulrazaq Kahya2
1Department of Mathematics
College of Education for Pure Sciences, University of Mosul
Mosul - Nineveh, IRAQ
2 Department of Computer Sciences
College of Education for Pure Sciences, University of Mosul
Mosul - Nineveh, IRAQ

Abstract

An approximate solution of the Fredholm integral equations (FIEs) of the second kind is obtained. The equations are converted into an unconstrained optimization problem. In this paper, an algorithm (BAC) for solving the Fredholm integral equations (FIEs), with a combination of Bees algorithm and Chebyshev polynomials, is presented. Chebyshev polynomials are first formulated, with undetermined coefficients, as an approximate solution of FIEs. These polynomials are replaced by the unknown function in the given Fredholm equation. The algorithm is in turn calculating the coefficients. Numerical examples are employed to approve the validity and the applicability of the proposed algorithm and the results are compared to the exact solution. The results show the efficiency and accuracy of the proposed algorithm to solve Fredholm integral equations (FIEs).

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

DOI: 10.12732/ijam.v35i6.4

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