Diagonal-implicitly iterated Runge-Kutta methods on distributed memory machines

We consider diagonal-implicitly iterated Runge-Kutta methods which are one- step methods for stiff ordinary differential equations providing embedded s olutions for stepsize control. In these methods, algorithmic parallelism is introduced at the expense of additional computations. In this paper, we co ncentrate on the algorithmic structure of these Runge-Kutta methods and con sider several parallel variants of the method exploiting algorithmic and da ta parallelism in different ways. Our aim is to investigate whether these v ariants lead to good performance on current distributed memory machines suc h as the Intel Paragon and the IBM SP2. As test application we use ordinary differential equations with dense and sparse right-hand side functions.