Entropy production by implicit Runge-Kutta schemes

Abstract

This paper follows up on the author's recent paper "Entropy Production by Explicit Runge-Kutta schemes", where a formula for the production of entropy by fully discrete schemes with explicit Runge-Kutta time integrators was presented. In this paper, the focus is on implicit Runge-Kutta schemes, for which the fully discrete numerical entropy evolution scheme is derived and tested.