We propose entropy-preserving and entropy-stable partitioned Runge-Kutta(RK) methods. In particular we develop entropy conditions for implicit-explicit methods and a class of second-order multirate methods. We extend relaxation ideas for explicit methods to partitioned RK methods. We show that the proposed methods support fully entropy-preserving and entropy-stability properties at a discrete level. Numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the behavior of these methods.

翻译：我们提议了酶-保护方法和酶-稳定分解龙格-库塔(RK)方法,特别是我们为隐含的显性方法和第二阶多流方法开发了酶条件和一类二阶多流方法,我们将对明确方法的放松想法扩大到分解的RK方法,我们表明拟议方法支持在离散水平上完全的酶-保存和酶-稳定特性。提出了普通差分方程和布尔格方程的数值结果,以显示这些方法的行为。