Abstract
A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partial derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Argyris and M. Haase,An Engineer’s Guide to Soliton Phenomena: Application of the Finite Element Method, Comput. Methods Appl. Mech. Engrg.61 (1987), 71–122.
A.G. Bratsos,The solution of the Boussinesq equation using the method of lines, Comput. Methods Appl. Mech. Engrg.157 (1998), 33–44.
R. Hirota,Exact N-soliton solutions of the wave of long waves in shallow-water and in nonlinear lattices, J. Math. Phys.14 (1973), 810–814.
V.S. Manoranjan, A.R. Mitchell and J.Li. Morris,Numerical solutions of the Good Boussinesq equation, SIAM J. Sci. Stat. Comput.5 (1984), 946–957.
C. Tomei,The Boussinesq equation, Ph.D. thesis, New York Univ., New York, 1982.
G.B. Whitham,Linear and Nonlinear Waves, New York, Wiley-Interscience, 1974.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bratsos, A.G. A parametric scheme for the numerical solution of the Boussinesq equation. Korean J. Comput. & Appl. Math. 8, 45–57 (2001). https://doi.org/10.1007/BF03011621
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03011621