Simple maximum principle preserving time-stepping methods for time-fractional Allen-Cahn equation

• Published in: Advances in computational mathematics Vol. 46; no. 2
• Main Authors: Ji, Bingquan, Liao, Hong-lin, Zhang, Luming
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2020; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Computer simulation; Finite element method; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Maximum principle; Visualization; 74A50; 65M06; Time-fractional Allen-Cahn equation; 35Q99; Discrete maximum principle; Fast L1 formula; Adaptive time-stepping strategy; Sharp error estimate; 65M12

Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo’s derivative. The time mesh is refined near the initial time to resolve the intrinsically initial singularity of solution, and u...