Variational Iteration Method for Solving Boussinesq Equations Using Maple

Abstract

In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. Several research papers have documented the values of the variational iteration method and its applications for various categories of differential equations. A comparison of the exact and numerical solutions was obtained using the variational iteration method. The variational iteration method shows that the proposed method is very effective and convenient. The results are shown for different specific cases of the problem. The variational iteration method is useful in numerical simulations and approximate analytical solutions, and it is used to resolve nonlinear differential equations in various situations using Maple. For example, the linear Boussinesq equation was resolved using the variational iteration method. By comparing the numerical results, we found that the variable repetition method produced accurate results and was close to the exact solution, allowing it to be widely applied to the Boussinesq equation. This proves the effectiveness of the method and the capability to quickly and effectively obtain the numerical number solution related to the exact solution using the Maple 18 program. Additionally, the outcomes are extremely precise.