Open AccessA Stabilized Fourier Spectral Method for the Fractional Cahn-Hilliard Equation
Author(s) -
Liquan Mei
Publication year - 2018
Publication title -
computer simulation in application
Language(s) - English
Resource type - Journals
ISSN - 2630-4597
DOI - 10.18063/csa.v1i3.907
Subject(s) - discretization , cahn–hilliard equation , mathematics , spectral method , fourier transform , energy (signal processing) , order (exchange) , mathematical analysis , fast fourier transform , space (punctuation) , fourier analysis , temporal discretization , stability (learning theory) , fourier series , algorithm , computer science , partial differential equation , statistics , finance , machine learning , economics , operating system
In this paper, the second order accurate (in time) energy stable numerical schemes are presented for the Fractional Cahn-Hilliard (CH) equation. Combining the stabilized technique, we apply the implicit Crank-Nicolson formula (CN) to derive second order temporal accuracy, and we use the Fourier spectral method for space discrete to obtain the fully discretization schemes. It is shown that the schemes are unconditionally energy stable. A few numerical experiments are presented to conclude the article.