AN EFFICIENT OPERATOR SPLITTING METHOD FOR A NORMALIZED TIME-FRACTIONAL ALLEN–CAHN EQUATION

Jian Wang, Qin Liu, Keyong Chen, Junxiang Yang, Ziwei Han, Soobin Kwak, Yunjae Nam, Seokjun Ham and Junseok Kim
Additional contact information
Jian Wang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Qin Liu: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Keyong Chen: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Junxiang Yang: School of Computer Science and Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Macao 999078, P. R. China
Ziwei Han: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China
Soobin Kwak: Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
Yunjae Nam: Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
Seokjun Ham: Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Republic of Korea

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-16

Abstract: In this paper, we propose a normalized time-fractional Allen–Cahn (TFAC) equation, in which a time-fractional derivative replaces the conventional derivative. We apply an efficient operator splitting technique to discretize the normalized TFAC equation. Compared to the conventional AC equation, the normalized TFAC equation features a unique time scale. This unique time scale provides an intuitive perspective on the fractional time derivative, as it represents a weighted average of the temporal history of the derivative. Moreover, the total integration of the weighting function is always 1 at all times. To study the dynamic characteristics of the computational solutions of the normalized TFAC equation, we investigated the mean curvature motion with a circular initial condition under different cases. Additionally, we applied the equation to more complex shapes to observe the differences in evolution over time between the normalized TFAC equation and the traditional AC equation. The experimental results show that the parameter significantly influences the numerical solutions. By adjusting the parameter, we can control the evolution rate to achieve the desired behavior.

Keywords: Normalized Time-Fractional Allen–Cahn Equation; Operator Splitting Method; Motion by Mean Curvature (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X25500859
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:33:y:2025:i:09:n:s0218348x25500859

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X25500859

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().