The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4693

Keywords:

System of Volterra Integral Equations (SVIEs), Homotopy Analysis Method (HAM), h-curves, Genetic Algorithm (GA).

Abstract

This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.

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Published

2023-04-30

How to Cite

Ahmed, R. F., Al-Hayani, W. M., & Al-Bayati, A. Y. (2023). The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions. European Journal of Pure and Applied Mathematics, 16(2), 864–892. https://doi.org/10.29020/nybg.ejpam.v16i2.4693

Issue

Vol. 16 No. 2: (April 2023)

Section

Nonlinear Analysis

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Copyright (c) 2023 European Journal of Pure and Applied Mathematics

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