Convergence aspects of step-parallel iteration of Runge-Kutta methods (Q1902089)

The nonlinear equations arising in the application of implicit Runge- Kutta methods (such as Radau IIA) have to be solved iteratively. One possibility to exploit parallel computer systems is to start the iterations in future steps already before convergence has been achieved in the actual step (parallelism across steps). This paper presents a convergence analysis (based on the test equation \(y'= \lambda y\)) for a special class of such step-parallel iteration methods.