Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31754
Cubic B-spline Collocation Method for Numerical Solution of the Benjamin-Bona-Mahony-Burgers Equation

Authors: M. Zarebnia, R. Parvaz


In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3444


[1] G. Stephenson, Partial Differential Equations for Scientists and Engineers, Imperial College Press, 1996.
[2] B. Wang, Random attractors for the stochastic BenjaminBonaMahony equation on unbounded domains, J. Differential Equations 246 (2009) 2506-2537.
[3] K. Al-Khaled, S. Momani, A. Alawneh, Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations, Applied Mathematics and Computation, 171 (2005) 281-292.
[4] M.A. Raupp, Galerkin methods applied to the Benjamin-Bona-Mahony equation, Bol Soc Brazil Mat 6 (1975), 65-77.
[5] J. Avrin, J.A. Goldstein, Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions, Nonlinear Anal. 9 (1985) 861-865.
[6] A.O. Celebi, V.K. Kalantarov, M. Polat, Attractors for the generalized Benjamin-Bona-Mahony equation, J. Differential Equations 157 (1999) 439-451.
[7] J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, third edition ,Springer-Verlg, 2002.
[8] D. Kincad, W. Cheny, Numerical analysis, Brooks/COLE, 1991.
[9] S.G. Rubin ,R.A. Graves, Cubic Spline Spproximation for Problems in Fluid Mechanics, NASA TR R-436, Washington, DC; 1975.
[10] G.D. Smith, Numerical Solution of Patial Differential Method, Second Edition, Oxford University Press, 1978.
[11] R.D Richtmyer, K.W. Morton, Difference Methods for Initial-Value Problems, Inter science Publishers (John Wiley), New York, (1967).
[12] L. R. T. Gardner, G. A. Gardner and I. Dag, A B-spline finite element method for the regularised long wave equation, Commun. Numer. Meth. Eng. 12 (1995) 795-804.