An Explicit Pseudo-Spectral Scheme with Almost Unconditional Stability for the Cahn-Hilliard Equation

Abstract

In this paper, an explicit fully discrete three-level pseudo-spectral scheme with almost unconditional stability for the Cahn-Hilliard equation is proposed. Stability and convergence of the scheme are proved by Sobolev's inequalities and the bounded extensive method of the nonlinear function (B.N. Lu (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 $u_0$ is investigated and the linear dispersive relation is obtained. Finally, the numerical results are supplied, which check the theoretical results. \u00a0