Vol.122, No.2, 2020, pp.743-756, doi:10.32604/cmes.2020.07996
OPEN ACCESS
RESEARCH ARTICLE
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: mahmoud.abdelrahman@mans.edu.eg; maabdelrahman@taibahu.edu.sa.
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)
Received 18 July 2019; Accepted 14 October 2019; 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., A., M., Almatrafi, M. B. (2020). Analytical and Numerical Investigation for the DMBBM Equation. CMES-Computer Modeling in Engineering & Sciences, 122(2), 743–756.