**Authors: **Younis A. Sabawi^{1 } & Supa B. Ahmed^{2 } & Hoshman Q. Hamad^{3 }

^{1}Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Koya, Iraq

^{1}Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq

^{2}Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq

^{3}Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Koya, Iraqq

**Abstract:** This paper aims to propose the semi implicit finite difference method for discretizing Cahn-Allen equation. The stability and convergence analysis are proved. It is shown that the suggest scheme is stable for the usage of the Fourier-Von Neumann technique. The accuracy of the proposed method is first order in time and second order in space. A comparison between the numerical and the exact solutions is supported with two examples. Numerical results are shown that there is a good agreement between the approximate solution and exact solution.

**Keywords:** Allen Equation, Semi Implicit Finite Difference, Stability of Allen Equation

**Published: June 2, 2022**

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