A numerical study of adding an artificial dissipation term for solving the nonlinear dispersive equations K(n,n)

Authors:
Tamer A. Abassy;H. El Zoheiry;Magdy A. El-Tawil
Affiliations:
Department of Scientific Computing, Faculty of Computers and Informatics, Benha University, Benha 13518, Egypt and Department of Mathematics, Faculty of Arts and Science in Wadi Addwasir, King Sau ...;Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt;Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

A linearized implicit finite difference method is devised for K(n,n). The stability and accuracy of the proposed methods are discussed. A compacton wave solution of the equation K(n,n) is used to examine the accuracy and efficiency of the proposed methods and study the effect of the added artificial dissipation term to solve the K(n,n) equation using finite difference method. The dynamics of waves having various initial wavepackets are discussed.