| 摘要: |
| Allen-Cahn方程是重要的相场模型, 在界面动力学问题研究中得到广泛应用.在时间和空间方向上使用Legendre-Gauss-Lobatto结点构造了Allen-Cahn方程的谱配置格式,并使用不动点迭代法求解所得非线性系统.丰富的数值算例验证了新算法的有效性. |
| 关键词: Allen-Cahn方程 非线性问题 谱配置法 |
| DOI：10.3969/J.ISSN.1000-5137.2023.03.002 |
| 分类号:O241.82 |
| 基金项目: |
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| Space-time spectral collocation method for Allen-Cahn equation |
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JIA Mengshu, XIE Shanshan, JIAO Yujian
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| Allen-Cahn equation is an important phase field model, which has been widely used to investigate interfacial dynamic problems. In this paper, we propose a Legendre-Gauss spectral collocation scheme for the Allen-Cahn equation by using Legendre-Gauss-Lobatto nodes as the collocation points in both the time and the space directions. We use the fixed point iteration method to solve the resulted nonlinear system. Ample numerical results demonstrate the efficiency of our new method. |
| Key words: Allen-Cahn equation nonlinear system space-time spectral collocation method |
