数学杂志2026，Vol.46Issue(1)：49-62,14.
Cahn-Hilliard方程的稳定化半隐格式切比雪夫谱方法
THE STABILIZED SEMI-IMPLICIT CHEBYSHEV SPECTRAL METHOD FOR THE CAHN-HILLIARD EQUATION
摘要
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.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Key words
Cahn-Hilliard equation/first-order stabilized semi-implicit scheme/second-order stabilized semi-implicit scheme/semi-implicit scheme/Chebyshev spectral method分类
数理科学引用本文复制引用
唐庶娟,罗贤兵..Cahn-Hilliard方程的稳定化半隐格式切比雪夫谱方法[J].数学杂志,2026,46(1):49-62,14.基金项目
国家自然科学基金资助(12461076). （12461076）
