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Spectral semi-discretization algorithm for a class of nonlinear parabolic PDEs with applications

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  • Izadi, Mohammad
  • Roul, Pradip

Abstract

This manuscript deals with a novel hybrid spectral collocation approach to find the approximate solutions of a class of nonlinear partial differential equations of parabolic type pertaining to various important physical models in mathematical biology. The problem under consideration arises in the study of propagation of gene and transmission of nerve impulses. A second-order time discretization algorithm based on Taylor series expansion is first employed to tackle the underlying nonlinearity of the problem. Then, the spectral collocation approach based on the alternative Laguerre polynomials (with positive coefficients) is adopted for approximation of the resulting semi-discrete ordinary differential equations. The convergence of the spectral technique is established. Three numerical test examples are given to demonstrate the applicability and efficiency of the proposed approach. The computed results are compared with the results obtained by other available methods in order to show the advantage of our method.

Suggested Citation

  • Izadi, Mohammad & Roul, Pradip, 2022. "Spectral semi-discretization algorithm for a class of nonlinear parabolic PDEs with applications," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322003009
    DOI: 10.1016/j.amc.2022.127226
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    References listed on IDEAS

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    1. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    2. Izadi, Mohammad & Srivastava, H.M., 2021. "Numerical approximations to the nonlinear fractional-order Logistic population model with fractional-order Bessel and Legendre bases," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Mohammad Izadi & Şuayip Yüzbaşi & Samad Noeiaghdam, 2021. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
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    Cited by:

    1. Tariq, Kalim U. & Wazwaz, Abdul-Majid & Javed, Rizwan, 2023. "Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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