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

The newly developed variable‐step L2‐1 σ 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.