Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic

@article{Noeiaghdam2018FindingOC,
  title={Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic},
  author={Samad Noeiaghdam and Mohammad Ali Fariborzi Araghi and Saeid Abbasbandy},
  journal={Numerical Algorithms},
  year={2018},
  pages={1-31}
}
The goal of this paper is to present a new scheme based on the stochastic arithmetic (SA) to find the optimal convergence control parameter, the optimal iteration and the optimal approximation of the homotopy analysis method (HAM). This scheme is called the CESTAC1 method. Also, the CADNA2 library is applied to implement the CESTAC method on the proposed algorithms. CADNA is able to present a new, robust and valid environment to implement the HAM and optimize the results. By using this method… CONTINUE READING
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