An efficient technique based on barycentric interpolation collocation method for the time fractional Allen-Cahn equation

This paper aims to numerically study two well-known difference formulas based on barycentric interpolation collocation method for the time fractional Allen-Cahn equation. The L1 formula and the fast convolution algorithm are used to approximate the Caputo time fractional derivative respectively, and the barycentric interpolation collocation method is applied to discretize the spatial derivative. Moreover, consistency analysis of semi-discretized in space and fully discretized nonlinear scheme is demonstrated. The nonlinear term is treated by explicit scheme to derive the discrete linear equations. Numerical experiments are presented to validate the theoretical results and show the configurations of phase field evolution.