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177344

Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials

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Last updated: 24 Dec 2024

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Abstract

We aim in this paper to develop a new algorithm for approximating the analytic solution for the integrodifferential equations using the Galerkin method. The bases of the solution obtained by the proposed algorithm are Chebyshev polynomials. Meanwhile, some theorems are deducted to simplify the nonlinear algebraic set resulted from applying the Galerkin method, while Newton's method is used to solve the resulting nonlinear algebraic system. Examples are introduced to prove the effectiveness of this algorithm in comparison with some other methods.

DOI

10.21608/erj.2021.177344

Keywords

Integro-differential equations, Chebyshev polynomials, Newton’s method, Gauss quadrature, Volterra, Fredholm

Authors

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M.

Last Name

Mostafa

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Affiliation

Physics and engineering mathematics department, Helwan University, Cairo, Egypt.

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First Name

Hesham

Last Name

A. M. A

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Physics and engineering mathematics department, Helwan University, Cairo, Egypt.

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First Name

W.

Last Name

Abbas

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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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Basic and applied science department, college of engineering and technology, Arab academy for science, technology and maritime transport, Cairo, Egypt.

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Volume

170

Article Issue

0

Related Issue

25477

Issue Date

2021-06-01

Receive Date

2021-06-13

Publish Date

2021-06-01

Page Start

169

Page End

183

Print ISSN

1110-5615

Article File

ERJ_Volume 170_Issue 0_Pages 169-183.pdf

PDF . 437.5kB

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https://erj.journals.ekb.eg/article_177344.html

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https://erj.journals.ekb.eg/service?article_code=177344

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Original Article

Type Code

998

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Publication Title

Engineering Research Journal

Publication Link

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

MainTitle

Galerkin Method for Nonlinear Volterra-Fredholm Integro-Differential Equations Based on Chebyshev Polynomials

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Article

Created At

22 Jan 2023