Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations. (7th June 2012)

• Record Type: Journal Article
• Authors: Zhao, Tinggang; Zhang, Xiaoxian; Huo, Jinxia; Su, Wanghui; Liu, Yongli; Wu, Yujiang
• Other Names: Otero-Espinar M. Victoria Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-06-07
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/106343
• Languages: English
• ISSNs: 1085-3375

Abstract

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.