The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we rigorously demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear fractional equations as tFAC equation on uniform meshes without any correction. Comparison with the classic fractional BDF2 and L2-1$_\sigma$ method further validates the superiority of SFTR in solving the tFAC equation. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results.

翻译：采用具有特殊平移量的平移分数阶梯形规则（SFTR）构造了时间分数阶Allen-Cahn（tFAC）方程的有限差分格式。首次揭示了SFTR权重的一些关键本质性质。基于这些性质，严格证明了该格式的离散能量衰减性质和极值原理保持性。数值研究表明，该格式能够在均匀网格上无需任何修正即可解决tFAC方程等非线性分数阶方程固有的初始奇异性。与经典分数阶BDF2及L2-1$_\sigma$方法的对比进一步验证了SFTR在求解tFAC方程中的优越性。关于离散能量衰减与离散极值原理的实验也证实了理论结果的正确性。