Stepsize restrictions for total-variation-boundedness in general Runge-Kutta procedures

In this paper, we propose a general theory yielding stepsize restrictions which cover a larger class of semi-discrete approximations than covered thus far in the literature. In particular, our theory gives stepsize restrictions, for general Runge-Kutta methods, which guarantee total-variation-boundedness in situations where the Euler process is TVB but not TVD.