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Title: Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations
Authors: Akrivis, G
Li, B 
Li, D
Issue Date: 2019
Source: SIAM journal on scientific computing, 2019, v. 41, no. 6, p. A3703-A3727
Abstract: We construct and analyze a class of extrapolated and linearized Runge–Kutta (RK) methods, which can be of arbitrarily high order, for the time discretization of the Allen–Cahn and Cahn–Hilliard phase field equations, based on the scalar auxiliary variable (SAV) formulation. We prove that the proposed q-stage RK–SAV methods have qth-order convergence in time and satisfy a discrete version of the energy decay property. Numerical examples are provided to illustrate the discrete energy decay property and accuracy of the proposed methods.
Keywords: Algebraic stability
Allen–Cahn equation
Cahn–Hilliard equation
Energy decay
Extrapolation
Gauss methods
Radau IIA methods
Runge–Kutta methods
Scalar auxiliary variable
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on scientific computing 
ISSN: 1064-8275
EISSN: 1095-7197
DOI: 10.1137/19M1264412
Rights: © 2019, Society for Industrial and Applied Mathematics.
Posted with permission of the publisher.
The following publication Akrivis, G., Li, B., & Li, D. (2019). Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations. SIAM Journal on Scientific Computing, 41(6), A3703-A3727 is available at https://dx.doi.org/10.1137/19M1264412
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