Convergence aspects of step-parallel iteration of Runge-Kutta methods Original Research Article

One of the most powerful methods for solving initial value problems for ordinary differential equations is an implicit Runge-Kutta method such as the Radau IIA methods. These methods are both highly accurate and highly stable. However, the iterative scheme needed for solving the implicit RK equations requires a lot of computational effort. The arrival of parallel computer systems has changed the situation in the sense that the effective computational effort can be reduced to a large extent. One option is the application of the iteration scheme concurrently at a number of step points on the t-axis. In this paper, we shall analyse the convergence of a special class of such step-parallel iteration methods.