  In the present work, we use the homotopy perturbation method (HPM) to solve
the Newell- Whitehead-Segel non-linear differential equations. Four case study
problems of Newell-Whitehead- Segel are solved by the HPM and the exact
solutions are obtained. The trend of the rapid convergence of the sequences
constructed by the method toward the exact solution is shown numerically. As a
result the rapid convergence towards the exact solutions of HPM indicates that,
using the HPM to solve the Newell-Whitehead-Segel non-linear differential
equations, a reasonable less amount of computational work with acceptable
accuracy may be sufficient. Moreover the application of the HPM proves that the
method is an effective and simple tool for solving the Newell-Whitehead-Segel
non-linear differential equations.
