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Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach
- Source :
- Numerical Algorithms, Numerical Algorithms, Springer Verlag, 2021, 88 (3), pp.1077-1108. ⟨10.1007/s11075-021-01068-y⟩
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In this paper, we propose and analyze high-order efficient schemes for the time-fractional Allen-Cahn equation. The proposed schemes are based on the L1 discretization for the time-fractional derivative and the extended scalar auxiliary variable (SAV) approach developed very recently to deal with the nonlinear terms in the equation. The main contributions of the paper consist of (1) constructing first- and higher order unconditionally stable schemes for different mesh types, and proving the unconditional stability of the constructed schemes for the uniform mesh; (2) carrying out numerical experiments to verify the efficiency of the schemes and to investigate the coarsening dynamics governed by the time-fractional Allen-Cahn equation. In particular, the influence of the fractional order on the coarsening behavior is carefully examined. Our numerical evidence shows that the proposed schemes are more robust than the existing methods, and their efficiency is less restricted to particular forms of the nonlinear potentials.
- Subjects :
- Discretization
Applied Mathematics
Numerical analysis
Scalar (physics)
Numerical Analysis (math.NA)
010103 numerical & computational mathematics
01 natural sciences
Stability (probability)
[SPI.MAT]Engineering Sciences [physics]/Materials
010101 applied mathematics
Nonlinear system
Theory of computation
FOS: Mathematics
Order (group theory)
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
Allen–Cahn equation
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 88
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....a6e9762539ad7dc3047903ab5729128e