Open Access

ARTICLE

Analytical and Numerical Investigation for the DMBBM Equation

Abdulghani Alharbi¹, Mahmoud A. E. Abdelrahman^{1, 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 the 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.

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