Runge-Kutta-Chebyshev Time Stepping for Parabolic Equations

We show progress towards developing an explicit Runge-Kutta-Chebyshev (RKC) time stepping method for multi-rate time stepping on adaptively refined, Cartesian meshes. Central to our investigation will be to show that RKC time stepping can be done efficiently and is competitive with standard implicit methods for parabolic equations. We show results in 1D, but eventually will incorporate RKC time stepping into ForestClaw, a library for solving PDEs on adaptively refined, multi-block quadtree meshes.