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396098

Using Legendre polynomials Formulas at Fresnel Integral Diffraction

Article

Last updated: 29 Dec 2024

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Abstract

Many advanced scientific phenomena of optics, light, and physics can be represented mathematically in the form of Volterra integral equations. In this paper, we studied the diffraction phenomena of the light beam. Since the most important category of scalar diffraction theories is the Fresnel diffraction integral. These integrals have been used in numerous studies on the propagation effects of structured light beams. These scalar diffraction theories have been widely utilized in

studying the propagation of structured light. finally, we applied first-kind shifted Legendre

polynomials to find the interpolate solutions of weakly singular Volterra integral equations of the

second kind, where the Fresnel integral of diffraction will be involved. Numerical examples have

been included in order to show the efficiency of the presented method. The exact solution of the represented example is compared to the approximate solution and the absolute error is calculated to illustrate the efficiency of the proposed method.

DOI

10.21608/jcsit.2024.332554.1012

Keywords

Volterra integral equations, Fresnel diffraction integral, Diffraction theory, Legendre Polynomials

Authors

First Name

Reham

Last Name

Gomaa

MiddleName

Abd Elsadek

Affiliation

Basic and applied science department, Faculty of Engineering, Arab academy for science, technology and maritime transport, Aswan, Egypt

Email

rehamd01291@m-eng.helwan.edu.eg

City

Aswan

Orcid

-

First Name

Ahmed

Last Name

Sayed

MiddleName

Yehia

Affiliation

Physics and Engineering Mathematics Department, Faculty of Engineering at Mataria, Helwan University, Cairo, Egypt.

Email

ahmed_badr@m-eng.helwan.edu.eg

City

Cairo

Orcid

0000-0001-5691-4993

First Name

Emil

Last Name

Shoukralla

MiddleName

Sobhi

Affiliation

Faculty of Electronic Engineering, Menofia University, Egypt

Email

shoukralla@el-eng.menofia.edu.eg

City

Cairo

Orcid

-

First Name

Alfaisal

Last Name

Hasan

MiddleName

Abd Elhameed

Affiliation

Basic and Applied Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Aswan, Egypt

Email

alfaisal772001@aast.edu

City

Aswan

Orcid

-

First Name

Nermin

Last Name

Saber

MiddleName

Abd Elsatar

Affiliation

Faculty of Energy and Environmental Engineering, British University in Egypt.

Email

nermin.saber@bue.edu.eg

City

Cairo

Orcid

-

Volume

6

Article Issue

1

Related Issue

51970

Issue Date

2024-12-01

Receive Date

2024-10-30

Publish Date

2024-12-01

Page Start

11

Page End

18

Print ISSN

2812-5630

Online ISSN

2812-5649

Link

https://jcsit.journals.ekb.eg/article_396098.html

Detail API

https://jcsit.journals.ekb.eg/service?article_code=396098

Order

396,098

Type

Original Article

Type Code

2,819

Publication Type

Journal

Publication Title

Journal of Communication Sciences and Information Technology

Publication Link

https://jcsit.journals.ekb.eg/

MainTitle

Using Legendre polynomials Formulas at Fresnel Integral Diffraction

Details

Type

Article

Created At

20 Dec 2024