Amirkabir University of TechnologyAUT Journal of Modeling and Simulation2588-295349220171201A Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation Method for Linear and Non-Linear Newell-Whitehead-Segel Equations22723899010.22060/miscj.2017.12051.4998ENS. S.NourazarDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranH.ParsaDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran0000-0002-3468-8419A.SanjariDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranJournal Article20161017In this paper, a comparison among the hybrid of Fourier Transform and Adomian<br />Decomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.<br />The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results are<br />compared with the exact solution. The comparison reveals that for the same number of components<br />of recursive sequences, the error of FTADM is much smaller than that of HPM. For the non-linear<br />NWS equation, the accuracy of FTADM is more pronounced than HPM. Moreover, it is shown that<br />as time increases, the results of FTADM, for the linear NWS equation, converges to zero. And for the<br />non-linear NWS equation, the results of FTADM converges to 1 with only six recursive components.<br />This is in agreement with the basic physical concept of NWS diffusion equation which is in turn in<br />agreement with the exact solution.https://miscj.aut.ac.ir/article_990_904b8331d108cdb9ea1cc3cdaaec53af.pdf