@Article{CSIAM-AM-4-1,
author = {Zhang, Hong and Xu, Qian and Xia, Jun and Songhe, Song},
title = {Unconditionally Maximum-Principle-Preserving Parametric Integrating Factor Two-Step Runge-Kutta Schemes for Parabolic Sine-Gordon Equations},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {1},
pages = {177--224},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0019},
url = {https://global-sci.com/article/82286/unconditionally-maximum-principle-preserving-parametric-integrating-factor-two-step-runge-kutta-schemes-for-parabolic-sine-gordon-equations}
}