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2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations

Author

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  • Hammad, D.A.
  • El-Azab, M.S.

Abstract

The generalized Burger’s–Huxley and Burger’s–Fisher equations are solved by fully different numerical scheme. The equations are discretized in time by a new linear approximation scheme and in space by 2N order compact finite difference scheme, after that a collocation method is applied. Also, the two-dimensional unsteady Burger’s equation is described by our proposed scheme. Numerical experiments and numerical comparisons are presented to show the efficiency and the accuracy of the proposed scheme.

Suggested Citation

  • Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:296-311
    DOI: 10.1016/j.amc.2015.02.009
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    Cited by:

    1. Hammad, D.A. & El-Azab, M.S., 2016. "Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 228-240.
    2. Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.
    3. Cosgun, Tahir & Sari, Murat, 2020. "Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Yang, Xiaojia & Ge, Yongbin & Zhang, Lin, 2019. "A class of high-order compact difference schemes for solving the Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 394-417.
    5. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.
    6. Yang, Xiaojia & Ge, Yongbin & Lan, Bin, 2021. "A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 510-534.

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