A fully discrete spectral scheme for time fractional Cahn-Hilliard equation with initial singularity. (1st December 2022)

• Record Type: Journal Article
• Authors: Chen, Li; Lü, Shujuan
• Is Part Of: Computers & mathematics with applications. Volume 127(2022)
• Page Start: 213
• Page End: 224
• Publication Date: 2022-12-01
• Subjects: Fractional Cahn-Hilliard equation -- Initial singularity -- Spectral method -- Stability -- Convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.10.015
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we study the numerical approximation of the time fractional Cahn-Hilliard equation with initial singularity. A nonlinear fully discrete scheme is constructed using the L2- 1 σ formula of time fractional order derivative on graded meshes and the Fourier spectral method in space. We present a priori estimate and give the existence and uniqueness of the approximate solution. The stability and convergence of the proposed scheme are proved rigorously. A numerical example is carried out to illustrate the theoretical analysis.