On the implementation of parallel iterated Runge-Kutta methods on a transputer network
The authors describe the implementation of an eighth-order parallel iterated Runge-Kutta formula (PIRK8) applied to initial value problems on different configurations of a transputer network. The PIRK8 method used is based on a four-stage Gauss-Legendre corrector, with variable step size, using a strategy similar to that of \textit{P. J. van der Houwen} and \textit{B. P. Sommeijer} [J. Comput. Appl. Math. 29, No. 1, 111-127 (1990; Zbl 0682.65039)]. The network topologies considered are four-ring, four-ring with separate head node, and fully connected with four nodes; each node represents a 20MHz transputer. Efficiency is compared with the corresponding sequential PIRK8 method. It is found that execution times are affected by the configuration used and the order in which the calculations are carried out. However, if the function evaluation cost is sufficiently high, the configuration is not very relevant.
eighth-order parallel iterated Runge-Kutta formula
scientific article; zbMATH DE number 459321