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122499

Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems

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Last updated: 04 Jan 2025

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Abstract

  In this paper, an efficient method based on the Galerkin technique for computing the eigenvalues and eigenfunctions for the second-order Sturm-Liouville problems. The first kind of Chebyshev polynomials ( ) is used as basis functions to solve this problem. The Chebyshev-Galerkin method is applied to reduce an ordinary differential equation into a system of algebraic equations using the orthogonality of Chebyshev polynomials and new relations driven from the orthogonality property. Numerical examples show that the proposed method is an easy method to implement and introduce accurate results.

DOI

10.21608/erj.2019.122499

Keywords

Chebyshev, Galerkin, Eigenvalues, Eigenfunctions, Sturm-Liouville

Authors

First Name

omar

Last Name

Mokhtar

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-

Affiliation

Physics and Engineering Mathematics Department, Faculty of Engineering, Mattaria, Helwan University, Egypt.

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First Name

wael

Last Name

Abbas

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-

Affiliation

Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt.

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First Name

Mohamed

Last Name

Fathy

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-

Affiliation

Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt.

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First Name

Ahmed

Last Name

A. M. Saidb,

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-

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Physics and Engineering Mathematics Department, Faculty of Engineering, Mattaria, Helwan University, Egypt.

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-

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-

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First Name

Hesham

Last Name

ahmed mohammed abd-EL Gawad

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-

Affiliation

Physics and Engineering Mathematics Department, Faculty of Engineering, Mattaria, Helwan University, Egypt.

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Volume

163

Article Issue

0

Related Issue

18331

Issue Date

2019-09-01

Receive Date

2020-11-10

Publish Date

2019-09-01

Page Start

27

Page End

42

Print ISSN

1110-5615

Article File

ERJ_Volume 163_Issue 0_Pages 27-42.pdf

PDF . 607.9kB

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https://erj.journals.ekb.eg/article_122499.html

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https://erj.journals.ekb.eg/service?article_code=122499

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Original Article

Type Code

998

Publication Type

Journal

Publication Title

Engineering Research Journal

Publication Link

https://erj.journals.ekb.eg/

MainTitle

Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems

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Article

Created At

22 Jan 2023