Approximate Analytic Solution of Newell-Whitehead-Segel Equation using Ara Transform Decomposition Method

Year 2026, Volume: 8 Issue: 1 , 1 - 17 , 28.04.2026

Julius Temitayo , Oludapo Olubanwo

https://doi.org/10.47087/mjm.1417467

https://izlik.org/JA79YP44CN

Abstract

This study applied the newly developed integral transform known as the ARA transform of order $n$ coupled with the Adomian Decomposition Method (AADM) employing Adomian polynomials to decompose the nonlinear component easily to obtain an approximation of the solution to Newell-Whitehead-Segel equation (NWSE). \begin{equation*} \frac{\partial \varphi(\mu,t)}{\partial t}=\ell^2\frac{\partial^2\varphi(\mu,t)}{\partial \mu^2}+\lambda_1\varphi(\mu,t)-\lambda_2\varphi^w(\mu,t)\label{e1} \end{equation*} A recurrence relation was obtained after combining this powerful method and was used to get each successive term which led to the formation of a series solution. About solving nonlinear differential equations, AADM is a potent technique as seen by the approximate and exact solution attained. The effectiveness of the suggested approach is demonstrated by solving three instances. The worthwhile conclusion reveals that the suggested approach is quite practical, uncomplicated, and applicable to linear and nonlinear real-world issues.

Keywords

Integral Transform , Nonlinear Differential Equation , ARA Transform

Ethical Statement

I affirm that all authors of the submitted research paper have directly participated in the planning, preparation, and analysis of the study

Supporting Institution

Olabisi Onabanjo University

Thanks

Thank you very much for your considedration

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