Abstract and Applied Analysis

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

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

Full-text: Open access

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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 106343, 22 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365125159

Digital Object Identifier
doi:10.1155/2012/106343

Mathematical Reviews number (MathSciNet)
MR2935137

Zentralblatt MATH identifier
1246.65176

Citation

Zhao, Tinggang; Zhang, Xiaoxian; Huo, Jinxia; Su, Wanghui; Liu, Yongli; Wu, Yujiang. Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 106343, 22 pages. doi:10.1155/2012/106343. https://projecteuclid.org/euclid.aaa/1365125159


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