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The Numerical Solution of the MRLW Equation Using the Multigrid Method
Mathematics Department, Faculty of Education and Science (AL-Khurmah Branch), Taif University, Taif, KSA
Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt
Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
- 1 Mathematics Department, Faculty of Education and Science (AL-Khurmah Branch), Taif University, Taif, KSA
- 2 Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt
- 3 Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
- 4 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
Applied Mathematics·Volume 05 (2014)·Pages 3328–3334·Published 1 December 2014·DOI10.4236/am.2014.521310
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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. 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.
KeywordsMultigrid MethodFinite Difference MethodMRLW Equation
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