الملخص

In this paper, Adomian Decomposition Method with Adomian polynomials are applied to solve Allen - Cahn equation with the initial condition only, also DuFort-Frankel method is applied with the initial and boundary conditions. The numerical results that are obtained by the Adomian decomposition method have been compared with the exact solution of  the equation shown that it is more efficient than the DuFort-Frankel method, that is illustrated through the tables and Figures.