Parallel solution of stiff ordinary differential equations

We consider the parallel solution of stiff ordinary differential equations with implicit Runge-Kutta (RK) methods. In particular, we describe parallel implementations of classical implicit RK methods and parallel implementations of diagonal-implicitly iterated RK (DIIRK) methods which have been especially developed for a parallel execution. DIIRK methods have computational redundancy but provide an additional source of parallelism in the form of independent nonlinear equation systems to be solved in each time step. To compare the runtimes of the parallel RK methods, we apply them to systems of ordinary differential equations resulting from a spatial discretization of partial differential equations. as programming, platform, we use a Gray T3E.