Allen-Cahn方程隐式Euler格式的长时间稳定性

Long-term Stability of the Implicit Euler Format of the Allen-Cahn Equation

Allen-Cahn方程是材料学中进行相场模拟的主要模型,其描述的是二元合金在一定温度下相位分离的过程.本文以带有Neumann边界的Allen-Cahn方程为研究对象,利用牛顿迭代法直接解由隐式Euler方法及有限差分法离散所得的非线性代数方程组.通过MATLAB进行数值实验,发现该方法是长时间稳定的.

The Allen-Cahn equation is the primary method simulating phase-field in materials science, which describes the process of a binary alloys at a certain temperature phase separation . In this paper, the Allen-Cahn equation with Neumann boundary was taken as the research object, and the Newton iterative method was used to directly solve the nonlinear equations obtained by the implicit Euler method and the finite difference method. The corresponding program was written by MATLAB and it was observed that the method is stable for a long time.