Exact and iterative solutions for DEs, including Fokker-Planck and Newell-Whitehead-Segel equations, using Shehu transform and HPM

This article proposes an iterative method using the Shehu Transform (ST) and the He’s Homotopy Perturbation Method (HPM). Integrating HPM with ST, this study addresses linear and nonlinear instances of equations like Fokker-Planck and Newell-Whitehead-Segel. The method shows reliability and precision through comparisons between exact and approximate results. The Shehu Transform Homotopy Perturbation Method (STHPM) is applied to these equations for the first time, with numerical and graphical comparisons made to HPM and the Elzaki Projected Differential Transform Method (EPDTM). Results demonstrate quick and accurate convergence, offering a robust alternative to traditional numerical methods. Future research explores extending this method to complex systems and real-world applications.

کلیدواژه ها:

Elzaki Projected Differential Transform (EPDT) ، He’s homotopy perturbation (HPM) ، Shehu Transformation ، Newell-Whitehead-Segel ، Fokker-Planck