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On the numerical investigations to the Cahn-Allen equation by using finite difference method.
- Source :
-
International Journal of Optimization & Control: Theories & Applications . Jan2019, Vol. 9 Issue 1, p18-23. 6p. - Publication Year :
- 2019
-
Abstract
- 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 L2 and L∞. 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21460957
- Volume :
- 9
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- International Journal of Optimization & Control: Theories & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134458477
- Full Text :
- https://doi.org/10.11121/ijocta.01.2019.00561