Optimal error estimate of Chebyshev-Legendre spectral method for the generalised Benjamin-Bona-Mahony-Burgers equations

DOI10.1155/2012/106343zbMath1246.65176OpenAlexW2086414740WikidataQ58694824 ScholiaQ58694824MaRDI QIDQ437503

Xiaoxian Zhang, Wanghui Su, Jinxia Huo, Yu-Jiang Wu, Yongli Liu, Tinggang Zhao

Publication date: 18 July 2012

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/106343

zbMATH Keywords

stabilitycomputational complexityconvergencenumerical experimentserror estimatesemidiscretizationBenjamin-Bona-Mahony-Burgers equationsChebyshev-Legendre spectral methodCrank-Nicolson/leapfrog scheme in time

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Complexity and performance of numerical algorithms (65Y20)

Related Items (5)

Time accurate solution to Benjamin-Bona-Mahony-Burgers equation via Taylor-Boubaker series scheme ⋮ A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin-Bona-Mahony-Burgers equation ⋮ L1 Fourier spectral methods for a class of generalized two-dimensional time fractional nonlinear anomalous diffusion equations ⋮ A new class of polynomial functions for approximate solution of generalized Benjamin-Bona-Mahony-Burgers (gBBMB) equations ⋮ On the convergence of difference schemes for the generalized BBM-Burgers equation

Uses Software

• Matlab

Cites Work

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• Chebyshev-Legendre pseudo-spectral method for the generalised Burgers-Fisher equation
• New periodic wave solutions via Exp-function method
• Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation
• Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution
• Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution
• Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations
• Exact solutions for the generalized BBM equation with variable coefficients
• Error analysis of Chebyshev-Legendre pseudo-spectral method for a class of nonclassical parabolic equation
• A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
• Convergence to diffusion waves of the solutions for benjamin-bona-mahony-burgers equations
• Sinc and solitary wave solutions to the generalized Benjamin–Bona–Mahony–Burgers equations
• A Fast Algorithm for the Evaluation of Legendre Expansions
• Spectral Methods and Their Applications
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points
• Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
• Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
• Optimal Error Estimates of the Chebyshev--Legendre Spectral Method for Solving the Generalized Burgers Equation
• Spectral Methods in MATLAB
• The Legendre Galerkin-Chebyshev collocation method for Burgers-like equations
• Decay of solution of generalized Benjamin—Bona—Mahony—Burgers equations in n-space dimensions
• Symmetry Analysis and Solutions for a Generalization of a Family of BBM Equations
• Finite difference discretization of the Benjamin‐Bona‐Mahony‐Burgers equation
• The Chebyshev–Legendre collocation method for a class of optimal control problems
• Model equations for long waves in nonlinear dispersive systems

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