Parallel execution of embedded and iterated Runge–Kutta methods

Abstract

In this paper, we consider the parallel solution of non-stiff ordinary differential equations with two different classes of Runge–Kutta (RK) methods providing embedded solutions: classical embedded RK methods and iterated RK methods which were constructed especially for parallel execution. For embedded Runge–Kutta methods, mainly the potential system parallelism is exploited. Iterated RK methods provide an additional source of parallelism in the form of independent function evaluations, but they usually require a higher number of function evaluations. We put the emphasis on the parallel execution time of these methods. Copyright © 1999 John Wiley & Sons, Ltd.