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Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations

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  • Tinggang Zhao
  • Xiaoxian Zhang
  • Jinxia Huo
  • Wanghui Su
  • Yongli Liu
  • Yujiang Wu

Abstract

Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. Optimal error estimate of the Chebyshev-Legendre method is proved for the problem with Dirichlet boundary condition. The convergence rate shows “spectral accuracy.†Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:106343
    DOI: 10.1155/2012/106343
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    Cited by:

    1. 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).

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