The Numerical Solution of the MRLW Equation Using the Multigrid Method

Yasser Mohamed Abo Essa; Ibrahim Abouefarag; El-Desouky Rahmo

doi:10.4236/am.2014.521310

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AM> Vol.5 No.21, December 2014

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The Numerical Solution of the MRLW Equation Using the Multigrid Method

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DOI: 10.4236/am.2014.521310 3,599 Downloads 4,130 Views Citations

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

Affiliation(s)

¹Mathematics Department, Faculty of Education and Science (AL-Khurmah Branch), Taif University, Taif, KSA.
²Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt.
³Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt.
⁴Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.

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. Using

error 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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Essa, Y. , Abouefarag, I. and 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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