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Numerical Resolution and Simulation of the Allen-Cahn Equation in the Two-Dimensional Case

Year: 2025

Type: article

Abstract: In this paper, we perform a resolution and simulation of the Allen-Cahn equation inn this article, we solve and simulate the Allen-Cahn equation in the two-dimensional case. This equation has been the basis of many theoretical and numerical studies. It should be noted that several techniques have been used to treat nonlinearity. In our specific case, we linearized this equation by approaching the nonlinear term by a limited Taylor series development in the vicinity of an initial reference solution. Numerical simulations carried out with the help of MATLAB software have highlighted the efficiency of the Allen-Cahn equation for modeling transition or phase separation phenomena in materials science.

Source: Journal of Advances in Mathematics and Computer Science

DOI: 10.9734/jamcs/2025/v40i41986

Authors: DJIBO Moustapha, MICHEL ÉLÉGBÉDÉ Olorunto Bienvenu, TRAORE Aboubakari, SALEY Bisso

Institution: Université Abdou Moumouni

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408740418

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