Analysis of Two Hybrid Schemes to Solve the Benjamin-Bona-Mahony (BBM) Equation

Abstract

In this research, we compare and contrast two numerical methods, the Laplace Adomian Decomposition Method (LADM) and the Elzaki Projected Differential Transform Method (EPDTM), for solving the Benjamin-Bona-Mahony (BBM) equation, and this helps in evaluating their performance, assessing robustness, gaining insights into solution behavior, validating results, generalizing their applicability, and advancing the field. This rigorous comparisons validates the efficacy of the methods as we compare the exact results and the results of LADM and EPDTM, plotting the convergent of the two methods to identify the method that is highly convergent and accurate. Results identify the Elzaki Projected Differential Transform Method (EPDTM) as having a simple and accurate numerical method for solving the BBM equation. EPDTM enhances accessibility, computational efficiency, accuracy, robustness, and validation of the solutions, supporting the understanding and analysis of wave phenomena described by the BBM equation. This study contributes to the advancement of the field of numerical analysis and computational science as practical applications of BBM equation in various fields, including coastal engineering, wave modeling, and wave stability analysis cannot be over emphasize.