A Novel Iterative Approach to Optimize the Banach Contraction Method for Solving Systems of Integro-Differential Equations

Thomas J.G.¹ , Okai J.O.² , Isah Abdullahi³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.6 , pp.75-85, Dec-2024

Online published on Dec 31, 2024

Copyright © Thomas J.G., Okai J.O., Isah Abdullahi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper presents an Optimized Banach Contraction Method (OBCM), which employs a novel iterative technique to solve integro-differential equations (IDEs) and their systems. The method offers a more efficient and faster approach than traditional methods, eliminating the need for discretization, linearization, or restrictive assumptions. It provides both analytical and approximate solutions for linear and nonlinear equations, without requiring the computation of polynomials or Lagrange multipliers. These advantages improve the reliability of the OBCM, with numerical results confirming its effectiveness.

Key-Words / Index Term :
Integro-differential equations (IDEs), Banach contraction principle, Variational iteration method, discretization, linearization

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