- Most sure precept and authentic power dissipation of arbitrarily high-order rescaled exponential time differencing Runge-Kutta schemes for Allen — Cahn equations
Authors: Chaoyu Quan, Xiaoming Wang, Pinzhong Zheng, Zhi Zhou
Summary: The power dissipation legislation and the utmost sure precept are two important bodily properties of the Allen — Cahn equations. Whereas many present time-stepping strategies are recognized to protect the power dissipation legislation, most apply to a modified type of power. On this work, we show that, when the nonlinear time period of the Allen — Cahn equation is Lipschitz steady, a category of arbitrarily high-order exponential time differencing Runge — Kutta (ETDRK) schemes protect the unique power dissipation property, underneath a light step-size constraint. Moreover, we assure the Lipschitz situation on the nonlinear time period by making use of a rescaling post-processing approach, which ensures that the numerical answer unconditionally satisfies the utmost sure precept. Consequently, our proposed schemes keep each the unique power dissipation legislation and the utmost sure precept and might obtain arbitrarily high-order accuracy. We additionally set up an optimum error estimate for the proposed schemes. Some numerical experiments are carried out to confirm our theoretical outcomes.
