Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods - Younis A. Sabawi; Supa B. Ahmed; Hoshman Q. Hamad (Eurasian Journal of Science and Engineering, 2022)
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.