The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions
Keywords:System of Volterra Integral Equations (SVIEs), Homotopy Analysis Method (HAM), h-curves, Genetic Algorithm (GA).
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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