Analytical Treatment of Abel Integral Equations by Optimal Homotopy Analysis Transform Method
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@Article{JICS-10-019,
author = {Mohamed S. Mohamed},
title = {Analytical Treatment of Abel Integral Equations by Optimal Homotopy Analysis Transform Method},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {10},
number = {1},
pages = {019--028},
abstract = { In this paper, a user friendly algorithm based on the optimal homotopy analysis transform
method (OHATM) is proposed to solve a system of generalized Abel's integral equations. The classical
theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the
approximate solutions converge to the exact solutions. Illustrative numerical examples are given to
demonstrate the efficiency and simplicity of the proposed method in solving such types of systems of Abel's
integral equations. Finally, several numerical examples are given to illustrate the accuracy and stability of
this method. Comparison of the approximate solution with the exact solutions we show that the proposed
method is very efficient and computationally attractive.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22561.html}
}
TY - JOUR
T1 - Analytical Treatment of Abel Integral Equations by Optimal Homotopy Analysis Transform Method
AU - Mohamed S. Mohamed
JO - Journal of Information and Computing Science
VL - 1
SP - 019
EP - 028
PY - 2024
DA - 2024/01
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22561.html
KW - integeral equation, Abel integral equation, optimal homotopy analysis transform method,
Laplace transform.
AB - In this paper, a user friendly algorithm based on the optimal homotopy analysis transform
method (OHATM) is proposed to solve a system of generalized Abel's integral equations. The classical
theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the
approximate solutions converge to the exact solutions. Illustrative numerical examples are given to
demonstrate the efficiency and simplicity of the proposed method in solving such types of systems of Abel's
integral equations. Finally, several numerical examples are given to illustrate the accuracy and stability of
this method. Comparison of the approximate solution with the exact solutions we show that the proposed
method is very efficient and computationally attractive.
Mohamed S. Mohamed. (2024). Analytical Treatment of Abel Integral Equations by Optimal Homotopy Analysis Transform Method.
Journal of Information and Computing Science. 10 (1).
019-028.
doi:
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