Exact and Iterative Solutions for DEs, Including Fokker-Planck and Newell-Whitehead-Segel Equations, Using Shehu Transform and HPM

Document Type : Research Paper

Authors

1 Department of Mathematics, Lahore Garrison University, Lahore, Pakistan.

2 School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China.

3 Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Menofia, Egypt.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 13 October 2024

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History

  • Receive Date: 21 May 2024
  • Revise Date: 27 September 2024
  • Accept Date: 06 October 2024

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