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Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

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  • Suheel Abdullah Malik
  • Ijaz Mansoor Qureshi
  • Muhammad Amir
  • Aqdas Naveed Malik
  • Ihsanul Haq

Abstract

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Suggested Citation

  • Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
    • Handle: RePEc:plo:pone00:0121728
    DOI: 10.1371/journal.pone.0121728
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. R. Nawaz & H. Ullah & S. Islam & M. Idrees, 2013. "Application of Optimal Homotopy Asymptotic Method to Burger Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, July.
    3. Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
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    Cited by:

    1. Singh, Harvindra & Balyan, L.K. & Mittal, A.K. & Saini, P., 2024. "A numerically robust and stable time–space pseudospectral approach for multidimensional generalized Burgers–Fisher equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 177-194.
    2. Azmat Ullah & Suheel Abdullah Malik & Khurram Saleem Alimgeer, 2018. "Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-18, January.

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