research-article

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

Authors:

Zhifeng WengAuthors Info & Claims

Numerical Algorithms, Volume 84, Issue 3

Pages 1155 - 1178

https://doi.org/10.1007/s11075-019-00795-7

Published: 01 July 2020 Publication History

Abstract

In this paper, we consider a fast explicit operator splitting method for a fractional Cahn-Hilliard equation with spatial derivative

{(- Δ)}^{\frac{α}{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

{(- Δ)}^{\frac{α}{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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Cited By

Huang XLi DLin XSun H(2025)A Fast Iterative Solver for Multidimensional Spatial Fractional Cahn-Hilliard EquationsJournal of Scientific Computing10.1007/s10915-025-02795-3102:3Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10915-025-02795-3
Huang XLi DSun HZhang F(2022)Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard EquationsJournal of Scientific Computing10.1007/s10915-022-01900-092:2Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/s10915-022-01900-0
Zhai SWeng ZFeng XHe Y(2021)Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal EquationJournal of Scientific Computing10.1007/s10915-020-01386-886:1Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10915-020-01386-8
Show More Cited By

Index Terms

Numerical approximation of the fractional Cahn-Hilliard equation by operator splitting method
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Numerical Algorithms

Numerical Algorithms Volume 84, Issue 3

Jul 2020

408 pages

ISSN:1017-1398

Issue’s Table of Contents

© Springer Science+Business Media, LLC, part of Springer Nature 2019.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 July 2020

Accepted: 08 August 2019

Received: 08 January 2019

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Cited By

Huang XLi DLin XSun H(2025)A Fast Iterative Solver for Multidimensional Spatial Fractional Cahn-Hilliard EquationsJournal of Scientific Computing10.1007/s10915-025-02795-3102:3Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10915-025-02795-3
Huang XLi DSun HZhang F(2022)Preconditioners with Symmetrized Techniques for Space Fractional Cahn-Hilliard EquationsJournal of Scientific Computing10.1007/s10915-022-01900-092:2Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/s10915-022-01900-0
Zhai SWeng ZFeng XHe Y(2021)Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal EquationJournal of Scientific Computing10.1007/s10915-020-01386-886:1Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10915-020-01386-8
Zhao YLi MOstermann AGu X(2021)An efficient second-order energy stable BDF scheme for the space fractional Cahn–Hilliard equationBIT10.1007/s10543-021-00843-661:3(1061-1092)Online publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1007/s10543-021-00843-6

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