Eurasian Journal of Science and Engineering (Jun 2022)
Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods
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.
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