On the numerical investigations to the Cahn-Allen equation by using finite difference method

Abstract

In this study, by using the finite difference method (FDM for short) and operators,the discretized Cahn-Allen equation is obtained. New initial condition for theCahn-Allen equation is introduced, considering the analytical solution given inApplication of the modified exponential function method to the Cahn-Allenequation, AIP Conference Proceedings 1798, 020033 [1]. It is shown that theFDM is stable for the usage of the Fourier-Von Neumann technique. Accuracy ofthe method is analyzed in terms of the errors in L 2 and L  . Furthermore, the FDMis treated in order to obtain the numerical results and to construct a table includingnumerical and exact solutions as well as absolute measuring error. A comparisonbetween the numerical and the exact solutions is supported with two and threedimensional graphics via Wolfram Mathematica 11.