A fully discrete spectral scheme for time fractional Cahn-Hilliard equation with initial singularity. (1st December 2022) - Chen, Li; Lü, Shujuan
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.