New Numerical Treatment for the Generalized Regularized Long Wave Equation Based on Finite Difference Scheme
Talaat S. EL-Danaf1, K. R. Raslan2, Khalid K. Ali3
1Talaat S. EL-Danaf, Department of Mathematics, Faculty of Science, Menoufia University, Shebein El-Koom,Egypt.
2K. R. Raslan , Department of Mathematics, Faculty of Science, AlAzhar University, Nasr-City, Cairo, Egypt. Khalid
3K. Ali, Department of Mathematics, Faculty of Science, AlAzhar University, Nasr-City, Cairo, Egypt..

Manuscript received on November 02, 2014. | Revised Manuscript received on November 04, 2014. | Manuscript published on November 05, 2014. | PP: 16-24 | Volume-4 Issue-5, November 2014. | Retrieval Number: D2328094414 /2014©BEIESP
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Abstract: In this paper, the generalized regularized long wave (GRLW) equation is solved numerically using the finite difference method. Fourier stability analysis of the linearized scheme shows that it is unconditionally stable. Also, the local truncation error of the method is investigated. Three invariants of motion are evaluated to determine the conservation properties of the problem, and the numerical scheme leads to accurate and efficient results. Moreover, interaction of two and three solitary waves is shown. The development of the Maxwellian initial condition into solitary waves is also shown and we show that the number of solitons which are generated from the Maxwellian initial condition can be determined. Numerical results show also that a tail of small amplitude appears after the interactions.
Keywords: Finite difference; generalized Regularized long wave equation; Solitary waves; Solitons.