Entropy-Preserving and Entropy-Stable Relaxation IMEX and Multirate Time-Stepping Methods
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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.
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