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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

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 equationsAdomian Decomposition MethodModified

References

A. O Nwaoburu(2020). Existence and uniqueness of the solution of non-linear integro-differential delay equation. International journal of pure and applied science, 11(9), 1660-5332. Adomian, G., & Rach, R. (1993). Modified decomposition solutions of linear and nonlinear boundary value problems. Mathematical and Computer Modelling, 18(12), 23-30. Asiya A. & Najmuddin A. (2023). Numerical accuracy of fredhomn of Fredholm Linear Integro Differential equation, using Adomain Decomposition Method, Modified Adomain Decomposition Method and Variational Iteration Method, Journal of Science and Art 23(3) 625-638 Golbabai, A., Ghorbani, A., & Talarposhti, R. A. (2020). Analytic Solution for the Nonlinear Integro-Differential Equations Arising in Engineering Problems by Modified Decomposition Method. Mathematics and Computers in Simulation, 176, 25–37. M. Rabbani & B. Zarali (2012). Solution of Fredholmn integro-differential equation by Modified Decomposition Method. The Journal of Mathematics and Computer Science 5(4) 258-264 Shams A. A. & Tarig M. E. (2020). On the comparative study of integro differential equation using different numerical methods. Journal of kings and sauds University-science, 32(1), 84-89. https://doi.org/10.1016/j.jksus.2018.03.003 Wazwaz, A. M. (2006). A New Method for Solving Singular Initial Value Problems in the Second- Order Ordinary Differential Equations. Applied Mathematics and Computation, 177(2), 644–652.

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