AN EXPLICIT PSEUDO-SPECTRAL SCHEME WHIT ALMOST UNCONDITIONAL STABILITY FOR THE CAHN-HILLIARD EQUATION

• 来源期刊: 计算数学（英文版）
• 关键词: Cahn-Hilliard equation Pseudo-spectral scheme Almost unconditional stability Linear stability for criticlal points Numerical experiments.
• 年，卷（期）: 2000,（2）
• 页码范围: 165-172
• 页数: 8页
• 语种: 英文

摘要

In this paper, an explicit fully discrete three-level pseudo-spectral scheme with almost unconditional stability for the Cahn-Hilliard equation is proposed. Stabil ity and convergence of the scheme are proved by Sobolev's inequalities and the bounded extensive method of the nonlinear function (B.N. Lu[4] (1995)). The scheme possesses the almost same stable condition and convergent accuracy as the Creak-Nicloson scheme but it is an explicit scheme. Thus the iterative method to solve nonlinear algebraic system is avoided. Moreover, the linear stability of the critical point u0 is investigated and the linear dispersive relation is obtained. Finally, the numerical results are supplied, which checks the theoretical results.