Partial Differential Equations in Applied Mathematics (Mar 2024)
Analytical approximate solutions to the nonlinear Fornberg–Whitham type equations via modified variational iteration method
Abstract
In this paper, we utilize the modified variational iteration method introduced by Abassy et al. for obtaining the analytical approximate solutions of the nonlinear Fornberg–Whitham equation and modified nonlinear Fornberg–Whitham equation. Here, we use the Maple 2021 software package for finding the analytical approximate solutions of the nonlinear Fornberg–Whitham equation and modified nonlinear Fornberg–Whitham equation and drawing their graphical representations. Moreover, here we provide a numerical comparison among the obtained analytical approximate solutions and exact solution for different particular cases. The obtained result of this paper confirm that the modified variational iteration method is more fruitful, straightforward, suitable and time consumed in repeated calculations than He's variational iteration method in case of finding analytical approximate solutions of the nonlinear Fornberg–Whitham equation and modified nonlinear Fornberg–Whitham equation.
