Before revision: [{\em  ] Experiments are run with implicit Runge-Kutta stages up to s=7, and it is found that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.
After revision: [{\em ] Experiments are run on two test problems, a 2D heat equation and a model advection-diffusion problem, using implicit Runge-Kutta stages up to s=7, and it is found that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.