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Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method

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Abstract

This paper develops an efficient numerical meshless method to solve the nonlinear generalized Burgers–Huxley equation (NGB-HE). The proposed method approximates the unknown solution in the two stages. First, the \(\theta\)-weighted finite difference technique is adopted to discretize the temporal dimension. Second, a combination of the multiquadric quasi-interpolation and pseudospectral (denoted by MQQI-PS) is constructed to approximate the spatial derivatives. In addition, a cross-validation technique is used to find the shape parameter value. Finally, numerical results are illustrated to show the accuracy and efficiency of the MQQI-PS method.

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Mahbubeh Rahimi, Hojatollah Adibi & Majid Amirfakhrian

  2. Department of Computer Science, University of Calgary, Calgary, Canada

    Majid Amirfakhrian

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  1. Mahbubeh Rahimi
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  2. Hojatollah Adibi
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  3. Majid Amirfakhrian
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Correspondence to Hojatollah Adibi.

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Rahimi, M., Adibi, H. & Amirfakhrian, M. Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method. Math Sci 17, 431–444 (2023). https://doi.org/10.1007/s40096-022-00461-5

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