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76689

A Computational Method for Solving Fredholm Integral Equations of the Second Kind

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Last updated: 25 Dec 2024

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Abstract

this paper presents a new double­-approximate computational method for solving Fredholm integral equations of the second kind. The method is based on the approximation of the given data function, and the unknown function by utilizing Legendre polynomials in matrix form, while the approximate function of Legendre coefficients of the first approximation of the kernel is expanded once again using Legendre polynomials. In addition, the double substitution of the unknown function into the considered integral equation provides access to a linear system of an algebraic equation, which is equivalent to the required solution. Convergence in the mean of the unknown function is proved. Finally, five illustrative examples are presented. It turns out that the obtained approximate solutions converge to the exact solutions that demonstrate the authenticity and the efficiency of the new method. 

DOI

10.21608/mjeer.2019.76689

Keywords

Fredholm integral equations, Legendre polynomials, approximate solution, second kind

Authors

First Name

Shoukralla,

Last Name

E. S.

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Affiliation

Deptartment.of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minufiya University Menouf, Egypt

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First Name

EL-Serafi,

Last Name

S. A.

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Deptartment.of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minufiya University Menouf, Egypt

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First Name

Elgohary,

Last Name

H.

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-

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Deptartment.of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minufiya University Menouf, Egypt

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First Name

Morgan,

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M.

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Deptartment..of Physics and Engineering Mathematics, Faculty of Engineering and Technology., GUC in Egypt Cairo, Egypt

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Volume

28

Article Issue

ICEEM2019-Special Issue

Related Issue

9704

Issue Date

2019-12-01

Receive Date

2020-03-10

Publish Date

2019-12-01

Page Start

280

Page End

285

Print ISSN

1687-1189

Online ISSN

2682-3535

Link

https://mjeer.journals.ekb.eg/article_76689.html

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https://mjeer.journals.ekb.eg/service?article_code=76689

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28

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Original Article

Type Code

1,088

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Journal

Publication Title

Menoufia Journal of Electronic Engineering Research

Publication Link

https://mjeer.journals.ekb.eg/

MainTitle

A Computational Method for Solving Fredholm Integral Equations of the Second Kind

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Article

Created At

22 Jan 2023