TY - EJOU AU - Alharbi, Abdulghani AU - Abdelrahman, Mahmoud A. E. AU - Almatrafi, M. B. TI - Analytical and Numerical Investigation for the DMBBM Equation T2 - Computer Modeling in Engineering \& Sciences PY - 2020 VL - 122 IS - 2 SN - 1526-1506 AB - 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. KW - DMBBM equation KW - Jacobian elliptic functions KW - moving mesh PDEs (MMPDEs) KW - moving adaptive scheme KW - solitary waves DO - 10.32604/cmes.2020.07996