Yasser Mohamed Abo Essa^1,2, Ibrahim Abouefarag^1,3, El-Desouky Rahmo^1,4

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¹ Mathematics Department, Faculty of Education and Science (AL-Khurmah Branch), Taif University, Taif, KSA.
² Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt.
³ Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt.
⁴ Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.
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Abstract: In this paper, we obtained the numerical solutions of the modified regularized long-wave (MRLW) equation, by using the multigrid method and finite difference method. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. The numerical solutions are compared with the known analytical solutions. Usingerror norms and conservative properties of mass, momentum and energy, accuracy and efficiency of the mentioned method will be established through comparison with other techniques.

Keywords: Multigrid Method, Finite Difference Method, MRLW Equation

Cite this paper: Essa, Y. , Abouefarag, I. , Rahmo, E. (2014) The Numerical Solution of the MRLW Equation Using the Multigrid Method. Applied Mathematics, 5, 3328-3334. doi: 10.4236/am.2014.521310.

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