Open AccessOptimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations
Author(s) -
Tinggang Zhao,
Zhang Xiao-xian,
Jinxia Huo,
Wanghui Su,
Liu Yong-li,
Yu-Jiang Wu
Publication year - 2012
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2012/106343
Subject(s) - mathematics , legendre polynomials , chebyshev filter , discretization , convergence (economics) , spectral method , rate of convergence , chebyshev iteration , chebyshev polynomials , dirichlet boundary condition , mathematical analysis , boundary value problem , computer science , channel (broadcasting) , economics , economic growth , computer network
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
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