A Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation Method for Linear and Non-Linear Newell-Whitehead-Segel Equations

In this paper, a comparison among the hybrid of Fourier Transform and Adomian Decomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated. The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results are compared with the exact solution. The comparison reveals that for the same number of components of recursive sequences, the error of FTADM is much smaller than that of HPM. For the non-linear NWS equation, the accuracy of FTADM is more pronounced than HPM. Moreover, it is shown that as time increases, the results of FTADM, for the linear NWS equation, converges to zero. And for the non-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 in agreement with the exact solution.