Analytical approximate solutions to the nonlinear Fornberg–Whitham type equations via modified variational iteration method

• Published in: Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2024-03, Vol.9, p.100631, Article 100631
• Main Authors: Asaduzzaman, Md, Özger, Faruk, Kilicman, Adem
• Format: Article
• Language: English
• Subjects: Analytical approximate solution; Maple 2021 software package; Modified nonlinear Fornberg–Whitham equation; Modified variational iteration method; Nonlinear Fornberg–Whitham equation
• ISSN: 2666-8181; 2666-8181
• DOI: 10.1016/j.padiff.2024.100631

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.