In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is much smaller than that of HPM. For the non-linearNWS equation, the accuracy of FTADM is more pronounced than HPM. Moreover, it is shown thatas time increases, the results of FTADM, for the linear NWS equation, converges to zero. And for thenon-linear NWS equation, the results of FTADM converges to 1 with only six recursive components.This is in agreement with the basic physical concept of NWS diffusion equation which is in turn inagreement with the exact solution.
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Nourazar et al. (2017) studied this question.