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A predictor-corrector scheme for the numerical solution of the Boussinesq equation

Abstract

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-liner system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

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Correspondence to M. S. Ismail.

Additional information

Athanassios Bratsos received his B.Sc. from the University of Athens, Greece and his M.Sc. and Ph.D from Brunel University, England, under the supervision of Prof. E.H. Twizell. Since 1984 he has been at the Technological Educational Institution (T.E.I.) of Athens, Greece, which elected him as a Professor of Mathematics. He is a member of IMACS. His research interests are at the numerical solution of linear/nonlinear partial differential equations.

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Ismail, M.S., Bratsos, A.G. A predictor-corrector scheme for the numerical solution of the Boussinesq equation. JAMC 13, 11 (2003). https://doi.org/10.1007/BF02936071

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  • DOI: https://doi.org/10.1007/BF02936071

AMS Mathematics Subject Classification

  • 65B05
  • 47H17
  • 49D15

Keyword and phrases

  • Boussinesq equation
  • soliton
  • finite-difference
  • predictor-corrector