IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 10 NO. 4 2024
DOI: 10.56201/ijasmt.v10.no4.2024.pg88.125

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Comparative Analysis of the Solution to Fredholm Linear Integro- Differential Equations by ADM, MADM and Series Expansion Method

Ejes, Valentine, Nwaoburu, Adols Okechukwu, Iyai, Davies

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Abstract

This study presents a comparative analysis of three methods for solving Fredholm linear integro- differential equations: the Adomian Decomposition Method (ADM), the Modified Adomian Decomposition Method (MADM), and the Series Expansion Method (SEM). These techniques are employed to derive approximate analytical solutions to equations that often resist exact analytical methods. The primary focus is to evaluate the accuracy, efficiency, and convergence of each method through theoretical analysis and practical examples. Graphs and tables are provided to illustrate the performance of these methods in solving selected problems. Our findings indicate that while each method has its strengths, MADM demonstrates superior accuracy in most cases, making it a promising tool for handling complex integro-differential equations in numerical analysis

keywords:

Fredholm integro-differential equations, Adomian Decomposition Method, Modified

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