The Allen-Cahn (AC) equation is solved by using various techniques and appears in many studies; Hariharan [
13] used Legendre wavelet-based approximation method to obtain an approximate solution of a few newell-whitehead (NW) and AC equations. Gui and Zhao [
14] obtained travelling wave solutions of AC equation by using fractional laplacian. Yokus and Bulut [
15] used the FDM to find a numerical solution for the AC equation. Javeed et al. [
16] implemented the first integral method to get an analytical solution for space-time fractional AC equation and coupled space-time fractional Drinfeld's Sokolov-Wilson system. Chen et al. [
12] proposed a time-space adaptive finite element method with the basis as 2nd-order, to solve the AC equation numerically. Hussain et al. [
11] used the homotopy analysis and perturbation approaches to find the approximate solution of the bistable AC equation. Yin [
17] proposed an algorithm for finite element (FE) method to get numerical solution of space fractional AC equation with continuous differentiable solutions. Li [
18] investigated a reduced-order finite difference (ROFD) iterative approach based on, proper orthogonal decomposition method for one dimensional nonlinear AC equation with a modest parameter perturbation, that meets two intrinsic properties of the AC equation: discrete maximum-bound-principle(DMBP)-preserving and discrete energy-stability(DES)-preserving. Li et al. [
19] investigated a ROFD technique for the AC equation with a minor parameter perturbation and a nonlinear factor concerned with the energy function. Khalid et al. [
20] proposed a numerical solution of time-fractional AC equation with the help of redefined cubic B spline functions and finite difference method. Olshanskii et al. [
21] investigated an equation of type AC defined on a surface that depends on time as a phase separation model in thin material along with the order-disorder transition. Ahmad et al. [
7] discussed diffusion equation and Cahn-Allen equation arising in oil pollution with integer-order and solved by using modified versions of variational iteration algorithms (MVIM-I).