The leading objective of this article is to investigate the analytical and numerical solutions of the Generalized Benjamin-Bona-Mahony (GBBM) equation. We also aim to compare the performance of the considered methods for solving this equation. The exact solution is obtained analytically while the numerical solutions are demonstrated using some techniques, namely, the adaptive moving mesh and uniform mesh methods. The exact solution is presented in a form of convergent power series. The finite differences are also applied to discretise the BBM equation. Under a suitable selection of parameters, some 2D and 3D surfaces for the obtained theoretical and numerical results are shown to compare the exact and numerical solutions.

本文的主要目的是研究广义本杰明-波纳-马洪尼（GBBM）方程的解析和数值解。我们还旨在比较所考虑方法求解该方程式的性能。通过解析获得精确解，同时使用一些技术（即自适应运动网格和均匀网格方法）演示数值解。确切的解决方案以收敛的幂级数形式表示。有限差分还用于离散BBM方程。下的参数的适当选择，示出了用于所获得的理论和数字结果一些2D和3D表面比较确切和数值解。