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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Applied Mathematics > Vol.5 No.21, December 2014

The Numerical Solution of the MRLW Equation Using the Multigrid Method ()

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

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.

DOI: 10.4236/am.2014.521310 PDF HTML XML 3,774 Downloads 4,304 Views Citations

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

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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