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This study considered the variation iteration method (VIM) and the homotopy perturbation method (HPM) for solving the Newell-Whitehead-Segel equation (NWSE). For this purpose, the Mamadu-Njoseh orthogonal polynomials were used as basis functions. Two cases of the NWSE were considered by variation of some parameters and with their analytic solutions given and formulated for numerical computations via VIM and HPM. Interesting results were obtained in the course of implementation and observed that the rate of convergence of solutions are controlled by the same parameters for both VIM and HPM iterative schemes. Further investigation revealed that the higher the values of these parameters, the faster the rate of convergence of the solutions for both methods. We presented the resulting numerical evidence in tables and graphs and our results compared with the analytic solutions as available in literature. Thus, we observed that the VIM and HPM have same rate of convergence for the various cases of the Newell-Whitehead-Segel equation considered. All computational frame works of this research were implemented with the aid of MAPLE 18.