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Analytical and Numerical Investigation for the DMBBM Equation

Abdulghani Alharbi1, Mahmoud A. E. Abdelrahman1, 2, *, M. B. Almatrafi1
1 Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia.
2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
* Corresponding Author: Mahmoud A. E. Abdelrahman.
   Email: ; .
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 122(2), 743-756. https://doi.org/10.32604/cmes.2020.07996

Received 18 July 2019; Accepted 14 October 2019; Issue published 01 February 2020

Abstract

The nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation is solved numerically using adaptive moving mesh PDEs (MMPDEs) method. Indeed, the exact solution of the DMBBM equation is obtained by using the extended Jacobian elliptic function expansion method. The current methods give a wider applicability for handling nonlinear wave equations in engineering and mathematical physics. The adaptive moving mesh method is compared with exact solution by numerical examples, where the explicit solutions are known. The numerical results verify the accuracy of the proposed method.

Keywords

DMBBM equation, Jacobian elliptic functions, moving mesh PDEs (MMPDEs), moving adaptive scheme, solitary waves.

Cite This Article

Alharbi, A., Abdelrahman, M. A. E., Almatrafi, M. B. (2020). Analytical and Numerical Investigation for the DMBBM Equation. CMES-Computer Modeling in Engineering & Sciences, 122(2), 743–756.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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