A Linear Fully Discrete Spectral Scheme for the Time Fractional Allen–Cahn Equation

This paper considers the numerical approximation of the time fractional Allen–Cahn equation with initial and periodic boundary conditions, and a linear fully discrete scheme is constructed with the finite difference method in time and the Fourier spectral method in space. Based on a temporal–spatial error splitting argument, the boundedness of numerical solutions in the L∞ norm is rigorously proved and the unconditional convergence of the proposed scheme is obtained. Numerical examples illustrate the theoretical results.