论文标题
时间裂纹的Cahn-Hilliard方程的不均匀时间稳定凸出方案
A Non-uniform Time-stepping Convex Splitting Scheme for the Time-fractional Cahn-Hilliard Equation
论文作者
论文摘要
在本文中，引入了用于求解广泛使用的时间裂缝的Cahn-Hilliard方程的非均匀时间stepping凸出的凸出数值算法。所提出的数值方案采用$ L1^+$公式来离散时间折叠式衍生物和二阶凸出技术来处理非线性术语，以半度性化处理。然后将伪谱法用于空间离散化。结果，完全离散的方案具有多个优点：二阶精确时间，在空间上精确，可唯一的解决，质量保存和无条件的能量稳定。给出了严格的证据，并获得了几个数值结果，以验证理论结果，并显示提出的方案的准确性和有效性。同样，已经研究了一些有趣的相分离动力学动力学。
In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn-Hilliard equation is introduced. The proposed numerical scheme employs the $L1^+$ formula for discretizing the time-fractional derivative and a second-order convex-splitting technique to deal with the non-linear term semi-implicitly. Then the pseudospectral method is utilized for spatial discretization. As a result, the fully discrete scheme has several advantages: second-order accurate in time, spectrally accurate in space, uniquely solvable, mass preserving, and unconditionally energy stable. Rigorous proofs are given, along with several numerical results to verify the theoretical results, and to show the accuracy and effectiveness of the proposed scheme. Also, some interesting phase separation dynamics of the time-fractional Cahn-Hilliard equation has been investigated.
