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A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems

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  • Al-Qudah, Alaa
  • Odibat, Zaid
  • Shawagfeh, Nabil

Abstract

In this study, an optimal homotopy analysis algorithm is outlined by means of the nonlinear reaction–diffusion systems. This algorithm, the linearization-based algorithm, employs Taylor series approximations of the nonlinear equations to construct an optimal decomposition of the homotopy series solutions. Numerical comparisons between the proposed algorithm and the standard homotopy approach, as tools for analytically solving reaction–diffusion systems, are performed to test the computational efficiency and the pertinent features of the suggested algorithm. The illustrated numerical results demonstrate that the linearization-based algorithm improves the accuracy and the convergence of the homotopy series solutions. The suggested algorithm can be further used to get rapid convergent series solutions for different types of systems of partial differential equations.

Suggested Citation

  • Al-Qudah, Alaa & Odibat, Zaid & Shawagfeh, Nabil, 2022. "A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 505-522.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:505-522
    DOI: 10.1016/j.matcom.2021.11.027
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    References listed on IDEAS

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    1. Sardanyés, Josep & Rodrigues, Carla & Januário, Cristina & Martins, Nuno & Gil-Gómez, Gabriel & Duarte, Jorge, 2015. "Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 484-495.
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    Cited by:

    1. Xiangcheng You & Shiyuan Li & Lei Kang & Li Cheng, 2023. "A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method," Energies, MDPI, vol. 16(5), pages 1-13, February.

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