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A new class of polynomial functions for approximate solution of generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equations

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  • Hajishafieiha, J.
  • Abbasbandy, S.

Abstract

In this paper, a new class of polynomial functions equipped with a parameter is used, which is applied to approximate the gBBMB. In this method, the first, time discretization of the gBBMB equations is made by using finite difference approaches. Then, at any spatial point, a nonlinear equations system is generated. Using the collocation points and solving a nonlinear system in the least squares method, the coefficients of functions are obtained. In some examples, a linearization is performed first, and then the collocation method is applied.

Suggested Citation

  • Hajishafieiha, J. & Abbasbandy, S., 2020. "A new class of polynomial functions for approximate solution of generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s009630031930757x
    DOI: 10.1016/j.amc.2019.124765
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    References listed on IDEAS

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    1. Zarebnia, M. & Parvaz, R., 2016. "On the numerical treatment and analysis of Benjamin–Bona–Mahony–Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 79-88.
    2. Tinggang Zhao & Xiaoxian Zhang & Jinxia Huo & Wanghui Su & Yongli Liu & Yujiang Wu, 2012. "Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-22, June.
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    Cited by:

    1. Ngondiep, Eric, 2024. "A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 560-577.
    2. Yüzbaşı, Şuayip & Yıldırım, Gamze, 2022. "A collocation method to solve the parabolic-type partial integro-differential equations via Pell–Lucas polynomials," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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