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

An International Journal of Optimization and Control: Theories & Applications

article

Asıf Yokus¹  Hasan Bulut² 

[1] Department of Actuarial, Fırat University;Department of Mathematics, Faculty of Science, Firat University

关键词: Cahn-Allen equation;    Finite Difference Method;    Numerical Solution;   

DOI  :  10.11121/ijocta.01.2019.00561

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

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 the Cahn-Allen equation is introduced, considering the analytical solution given in Application of the modified exponential function method to the Cahn-Allen equation, AIP Conference Proceedings 1798, 020033 [1]. It is shown that the FDM is stable for the usage of the Fourier-Von Neumann technique. Accuracy of the method is analyzed in terms of the errors in and Furthermore, the FDM is treated in order to obtain the numerical results and to construct a table including numerical and exact solutions as well as absolute measuring error. A comparison between the numerical and the exact solutions is supported with two and three dimensional graphics via Wolfram Mathematica 11.

【 授权许可】

CC BY