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. 11 NO. 1 2025
DOI: 10.56201/ijasmt.vol.11.no1.2025.pg34.50

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Comparative Analysis of the Solution to Fredholm Linear Integro Differential Equation by VIA and SEM

Ejes, Valentine

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Abstract

This study presents a comparative analysis of the Variational Iteration Method (VIM) and the Series Expansion Method (SEM) for solving Fredholm Integro-Differential Equations (FIDEs). Both methods were applied to an illustrative example, showcasing their effectiveness in addressing this class of equations. While SEM provided approximate solutions with acceptable accuracy, VIM demonstrated a distinct advantage by delivering exact solutions. The performance of the methods was evaluated through numerical experiments, with results presented using graphs and tables for clarity. SEM, though straightforward in its approach, exhibited slower convergence and reduced precision. On the other hand, VIM, employing correction functionals and Lagrange multipliers, consistently achieved high accuracy with minimal computational effort. The findings confirm that while both methods are effective, VIM is the more reliable and efficient approach for solving FIDEs. Its ability to produce exact solutions highlights its suitability for practical applications in mathematics and engineering.

keywords:

Fredholm integro-differential equations, Variational Iteration method and Series

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References:

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