Linearized Fractional Adams Scheme for Fractional Allen–Cahn Equations

Abstract

The objective of this work is to solve the fractional Allen–Cahn equations (ACEs) using a method that combines the modified Rubin–Graves linearization scheme and the implicit higher-order Adams–Moulton (AM) scheme to resolve the difficulties induced by the fractional derivatives and the nonlinearity of the given fractional Allen–Cahn equations. The fractional derivative is taken into Caputo's sense. Additionally, the second-order central finite difference (FD) scheme is used for spatial discretization. The convergence of the proposed method is theoretically and numerically discussed. Its efficiency is verified via several numerical experiments and compared with that of existing methods.