Numerical solution of Fredholm integral equation of the first kind with degenerated kernel by using Hermite polynomial

Hassan, Talhat I.; Sulaiman, Najmaddin A.

doi:10.33899/edusj.2006.77250

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Fredholm Integral Equation Of the 2nd Kind1

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2022

2023

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“…with the unknown function y(x) and the kernel function K(x, t), which are bounded in the square a ≤ x ≤ b and a ≤ t ≤ b. They can be characterized by upper and lower constant bounds a and b respectively, in the integration [16,17].…”

Section: Fredholm Integral Equation Of the 2nd Kindmentioning

confidence: 99%

Solving Fredholm Integral Equations Using Bees Algorithm Based on Chebyshev Polynomials

Aladool¹,

Kahya²

2023

Int. J. of Appl. Math.

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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).

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Section: Fredholm Integral Equation Of the 2nd Kindmentioning

confidence: 99%