Unconditionally Maximum Bound Preserving and Original Energy Dissipative Arbitrarily High-Order Rescaled Exponential Time Differencing Runge-Kutta Schemes for Allen-Cahn Equations

Arbitrarily high-order rescaled exponential time differencing Runge-Kutta (ETDRK) schemes are developed that unconditionally preserve the maximum bound principle and the original energy dissipation law for the Allen-Cahn equation.