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

This study applied the newly developed integral transform known as the ARA transform oforder $n$ coupledwith the Adomian Decomposition Method (AADM)employing Adomian polynomials to decompose the nonlinear component easily toobtainan 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 usedto get each successiveterm which led to the formation of a series solution. Aboutsolving nonlinear differential equations, AADM is a potent technique as seen by the approximate and exactsolution 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 tolinear and nonlinear real-world issues.