Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods

Authors: Younis A. Sabawi1 & Supa B. Ahmed2 & Hoshman Q. Hamad3
1Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Koya, Iraq
1Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq
2Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq
3Department 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

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Doi: 10.23918/eajse.v8i1p90

Published: June 2, 2022


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