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Title: Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
Authors: Zhang, Hong
Yan, Jingye
Qian, Xu
ong, Songhe
Keywords: Science::Mathematics
Issue Date: 2022
Source: Zhang, H., Yan, J., Qian, X. & ong, S. (2022). Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations. Computer Methods in Applied Mechanics and Engineering, 393, 114817-.
Journal: Computer Methods in Applied Mechanics and Engineering
Abstract: We propose and analyze a class of temporal up to fourth-order unconditionally structure-preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first revisit some up to second-order exponential time different Runge–Kutta (ETDRK) schemes, and provide unified proofs for the unconditionally maximum-principle-preserving and mass-conserving properties. Noting that the stabilized ETDRK schemes belong to a special class of parametric Runge–Kutta schemes, we introduce the stabilized integrating factor Runge–Kutta (sIFRK) formulation to construct new high-order parametric single-step methods, and propose two strategies to eliminate the exponential effects of sIFRK: (1) a recursive approximation; (2) a combination of exponential and linear functions. Together with the nonnegativity of coefficients and non-decreasing of abscissas, the resulting two families of improved stabilized integrating factor Runge–Kutta (isIFRK) schemes can unconditionally preserve the maximum-principle and conserve the mass. The order conditions, linear stability and convergence in the l∞-norm are analyzed rigorously. We demonstrate that the proposed framework, which is explicit and free of limiters or cut-off post-processing, offers a simple, practical, and effective approach to developing high-order unconditionally structure-preserving algorithms. Comparisons with traditional schemes demonstrate the necessity of developing high-order unconditionally structure-preserving schemes. A series of numerical experiments verify theoretical results of proposed isIFRK schemes.
ISSN: 0045-7825
DOI: 10.1016/j.cma.2022.114817
Rights: © 2022 Elsevier B.V. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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