| 摘要: |
| 本文研究了Cahn-Hilliard方程的三种不同的数值格式：半隐式格式,一阶稳定化半隐格式, 二阶稳定化半隐格式的问题.利用切比雪夫谱方法进行空间离散, 有限差分法对时间离散的方法,得到Cahn-Hilliard方程的数值离散格式. 在数值实验中, 验证了当数值解达到稳定时, 对于不同的稳定化常数S, 稳定格式所需时间步长相较于非稳定格式的1000倍. 该方法验证了切比雪夫谱方法求解三种数值格式的有效性. |
| 关键词: Cahn-Hilliard方程 一阶稳定化半隐格式 二阶稳定化半隐格式 半隐格式 切比雪夫谱方法 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家自然科学基金资助(12461076). |
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| THE STABILIZED SEMI-IMPLICIT CHEBYSHEV SPECTRAL METHOD FOR THE CAHN-HILLIARD EQUATION |
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TANG Shu-juan, LUO Xian-bing
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School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
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| Abstract: |
| This study investigates three distinct numerical schemes for the Cahn-Hilliard equation: the semi-implicit scheme, the first-order stabilized semi-implicit scheme, and the second-order stabilized semi-implicit scheme. A hybrid approach combining the Chebyshev spectral method (for space) and finite differences (for time) is proposed to discretize the Cahn-Hilliard equation. Numerical experiments demonstrate that when the numerical solution reaches a steady state, the stabilized schemes allow time steps up to 1000 times larger than those of the non-stabilized scheme for different stabilization constants S. This study validates the effectiveness of the Chebyshev spectral method for solving all three numerical schemes. |
| Key words: Cahn-Hilliard equation first-order stabilized semi-implicit scheme second-order stabilized semi-implicit scheme semi-implicit scheme Chebyshev spectral method |
