Maximum-Bound-Principle-Preserving Predictor–Corrector Methods for the Time-Fractional Allen–Cahn Equation With General Nonlinear Potential

The newly developed variable-step L2-1σ numerical framework successfully achieves simultaneous retention of the energy dissipation property and bound-preserving criterion for the time-fractional Allen–Cahn equation with a double-well potential. In this work, we further extend this scheme by incorporating the predictor–corrector methodology, enabling the extended algorithm to not only uphold the maximum bound principle for the time-fractional Allen–Cahn equation involving general nonlinear potentials, but also retain a linear-implicit structure along with a second-order temporal convergence rate. Comprehensive numerical experiments are conducted in the end to verify the numerical precision, computational efficiency, and long-term bound-preserving performance of the proposed approach.