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Numerical Algorithms

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23-08-2019 | Original Paper

Numerical approximation of the fractional Cahn-Hilliard equation by operator splitting method

Authors: Shuying Zhai, Longyuan Wu, Jingying Wang, Zhifeng Weng

Published in: Numerical Algorithms | Issue 3/2020

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Abstract

In this paper, we consider a fast explicit operator splitting method for a fractional Cahn-Hilliard equation with spatial derivative \((-{\varDelta })^{\frac {\alpha }{2}}\)(α ∈ (1,2]), where the choice α = 2 corresponds to the classical Cahn-Hilliard equation. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudo-spectral method is adopted, and thus an ordinary differential equation is obtained. For the nonlinear part, a second-order SSP-RK method together with the pseudo-spectral method is used. The stability and convergence of the proposed method in L²-norm are studied. We also carry out a comparative study of two classical definitions for fractional Laplacian \((-{\varDelta })^{\frac {\alpha }{2}}\), and numerical results obtained using computational simulation of the fractional Cahn-Hilliard equation for a variety of choices of fractional order α are presented. It is observed that the fractional order α controls the sharpness of the interface, which is typically diffusive in integer-order phase-field models.

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Title: Numerical approximation of the fractional Cahn-Hilliard equation by operator splitting method
Authors: Shuying Zhai
Longyuan Wu
Jingying Wang
Zhifeng Weng
Publication date: 23-08-2019
Publisher: Springer US
Published in: Numerical Algorithms / Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00795-7

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