Skip to main content

A parametric scheme for the numerical solution of the Boussinesq equation

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, access via your institution.

References

  1. 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.

    MATH  Article  MathSciNet  Google Scholar 

  2. A.G. Bratsos,The solution of the Boussinesq equation using the method of lines, Comput. Methods Appl. Mech. Engrg.157 (1998), 33–44.

    MATH  Article  MathSciNet  Google Scholar 

  3. 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.

    MATH  Article  MathSciNet  Google Scholar 

  4. 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.

    MATH  Article  MathSciNet  Google Scholar 

  5. C. Tomei,The Boussinesq equation, Ph.D. thesis, New York Univ., New York, 1982.

    Google Scholar 

  6. G.B. Whitham,Linear and Nonlinear Waves, New York, Wiley-Interscience, 1974.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Bratsos.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03011621

AMS Mathematics Subject Classification

  • 65J15
  • 47H17
  • 49D15

Keyword and phrases

  • Boussinesq equation
  • soliton
  • finite-difference
  • linearized