Numerical Resolution and Simulation of the Allen-Cahn Equation in the Two-Dimensional Case

In this paper, we perform a resolution and simulation of the Allen-Cahn equation inn this article, we solve and simulate the Allen-Cahn equation in the two-dimensional case. This equation has been the basis of many theoretical and numerical studies. It should be noted that several techniques have been used to treat nonlinearity. In our specific case, we linearized this equation by approaching the nonlinear term by a limited Taylor series development in the vicinity of an initial reference solution. Numerical simulations carried out with the help of MATLAB software have highlighted the efficiency of the Allen-Cahn equation for modeling transition or phase separation phenomena in materials science.