Solving Linear System of Fredholm Integral Equations with Homotopy Analysis and Genetic Algorithms

Abstract

In this paper, we propose a technique called Homotopy Analysis Method (HAM) for solving linear systems of Fredholm integral equations to find relatively close solutions. The HAM approach involves an auxiliary parameter that offers a straightforward method for adjusting and managing the region where the series of solutions converge. We demonstrate the effectiveness of the HAM approach through our experimental results. Additionally, we improve the HAM approach by incorporating a genetic algorithm (HAM-GA) to further optimize the solutions. The performance of HAM-GA is evaluated by comparing its results to those obtained by HAM, using the residual error function as a fitness function for the genetic algorithm.