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Journals / Hacettepe Journal of Mathematics and Statistics / 2015 / Cilt: 44 - Sayı: 1

A new efficient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind

Y. KHAN
M. FARDI
Pages
93–99
Publication Date
2022-10-18
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

Two examples are presented to illustrate the accuracy and effectiveness of the proposed approach. 2000 AMS Classifi cation: 45B05

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a new multi-parametric homotopy approach is proposed to find the approximate solution of linear and non-linear two-dimensional Fredholm integral equations of the second kind.
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Key Findings & Data:In this framework, convergence of the proposed approach for these types of equations is investigated.
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Conclusion & Impact:Two examples are presented to illustrate the accuracy and effectiveness of the proposed approach. 2000 AMS Classifi cation: 45B05
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Domain Parameters

Abstract

In this paper, a new multi-parametric homotopy approach is proposed to find the approximate solution of linear and non-linear two-dimensional Fredholm integral equations of the second kind. In this framework, convergence of the proposed approach for these types of equations is investigated. This homo- topy contain two auxiliary parameters that provide a simple way of controlling the convergence region of series solution. The results of present method are compared with Adomian decomposition method (ADM) results which provide confirmation for the validity of proposed approach. Two examples are presented to illustrate the accuracy and effectiveness of the proposed approach. 2000 AMS Classifi cation: 45B05

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Cite This Article

KHAN, Y., FARDI, M. (2022). A new efficient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 93–99. https://ajindex.com/articles/530214

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