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| 摘要: |
| 这篇文章主要是采用切比雪夫谱方法求解Cahn-Hilliard方程，并引入该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。并用切比雪夫谱方法进行空间离散，在时间上用半隐式方法离散，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，即验证了该方法的有效性。 |
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| Abstract: |
| This study primarily employs the Chebyshev spectral method to solve the Cahn-Hilliard equation and introduces three distinct numerical schemes for this equation: the semi-implicit scheme, the first-order stabilized semi-implicit scheme, and the second-order stabilized semi-implicit scheme. The Cahn-Hilliard equation is discretized in space using the Chebyshev spectral method and in time using a semi-implicit scheme, yielding its numerical discretization. Numerical experiments confirm that, at steady state, the stabilized scheme permits a time step 1000 times greater than the non-stabilized version under varying stabilization constants S, validating the method's efficacy. |
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