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24320

NUMERICAL SOLUTIONS OF SINGULAR INITIAL VALUE PROBLEMS IN THE SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING HYBRID ORTHONORMAL BERNSTEIN AND BLOCK-PULSE FUNCTIONS

Article

Last updated: 22 Jan 2023

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Abstract

Orthonormal Bernstein coupled with Block-Pulse Functions for integro-differential form of the singular Emden-
Fowler initial value problems, is considered. First, we introduce the proposed method then the singular differential
equations are transformed to Volterra integro-differential equations. We transform the obtained equations to
algebraic system of equations. Solution to the problem is identified by solving this system and the constructed
solutions are of approximation form. We compare the results with exact solutions and other methods to show the
accuracy of proposed method. The obtained results guarantee the method provides an approximate solution to the
generalized singular Lane-Emden type equations.

DOI

10.21608/JOEMS.2018.9471

Keywords

Hybrid orthonormal Bernstein and Block-Pulse Functions, Convergence analysis, Lane–Emden equation, Gaussian integrations

Authors

First Name

Mohamed

Last Name

Ramadan

MiddleName

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Affiliation

Department of Mathematics, Faculty of Science, Menoufia University, Egypt

Email

mramadan12@yahoo.com

City

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Orcid

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First Name

Adel

Last Name

Hadhoud

MiddleName

-

Affiliation

Department of Mathematics, Faculty of Science, Menoufia University, Egypt

Email

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City

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Orcid

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First Name

Mohamed

Last Name

Ali

MiddleName

-

Affiliation

Department of Mathematics, Faculty of Engineering, Benha University, Egypt

Email

-

City

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Orcid

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Volume

26

Article Issue

1

Related Issue

4436

Issue Date

2018-01-01

Receive Date

2017-06-12

Publish Date

2018-01-01

Page Start

156

Page End

166

Print ISSN

1110-256X

Online ISSN

2090-9128

Link

https://joems.journals.ekb.eg/article_24320.html

Detail API

https://joems.journals.ekb.eg/service?article_code=24320

Order

14

Type

Original Article

Type Code

485

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

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Article

Created At

22 Jan 2023