TY - JOUR
T1 - Unconditionally Maximum-Principle-Preserving Parametric Integrating Factor Two-Step Runge-Kutta Schemes for Parabolic Sine-Gordon Equations
AU - Zhang , Hong
AU - Qian , Xu
AU - Xia , Jun
AU - Song , Songhe
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 177
EP - 224
PY - 2023
DA - 2023/01
SN - 4
DO - http://doi.org/10.4208/csiam-am.SO-2022-0019
UR - https://global-sci.org/intro/article_detail/csiam-am/21340.html
KW - Parabolic sine-Gordon equation, linear-invariant-conserving, unconditionally maximum-principle-preserving, parametric two-step Runge-Kutta method.
AB - <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>