Unconditionally Maximum-Principle-Preserving Parametric Integrating Factor Two-Step Runge-Kutta Schemes for Parabolic Sine-Gordon Equations
Year: 2023
Author: Hong Zhang, Xu Qian, Jun Xia, Songhe Song
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 177–224
Abstract
We present a systematic two-step approach to derive temporal up to the eighth-order, unconditionally maximum-principle-preserving schemes for a semilinear parabolic sine-Gordon equation and its conservative modification. By introducing a stabilization term to an explicit integrating factor approach, and designing suitable approximations to the exponential functions, we propose a unified parametric two-step Runge-Kutta framework to conserve the linear invariant of the original system. To preserve the maximum principle unconditionally, we develop parametric integrating factor two-step Runge-Kutta schemes by enforcing the non-negativeness of the Butcher coefficients and non-decreasing constraint of the abscissas. The order conditions, linear stability, and convergence in the $L^∞$-norm are analyzed. Theoretical and numerical results demonstrate that the proposed framework, which is explicit and free of limiters, cut-off post-processing, or exponential effects, offers a concise, and effective approach to develop high-order inequality-preserving and linear-invariant-conserving algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2022-0019
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 177–224
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 48
Keywords: Parabolic sine-Gordon equation linear-invariant-conserving unconditionally maximum-principle-preserving parametric two-step Runge-Kutta method.