On the implementation of parallel iterated Runge-Kutta methods on a transputer network
type: Item
instance of: scholarly article
title: On the implementation of parallel iterated Runge-Kutta methods on a transputer network
zbMATH Open document ID: 0786.65059
DOI: 10.1016/0168-9274(93)90139-I
published in: Applied Numerical Mathematics
publication date: 1994-01-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 459321
zbMATH Keywords: parallel algorithms
zbMATH Keywords: eighth-order parallel iterated Runge-Kutta formula
zbMATH Keywords: initial value problems
zbMATH Keywords: transputer network
zbMATH Keywords: PIRK8 method
zbMATH Keywords: four-stage Gauss-Legendre corrector
zbMATH Keywords: variable step size
author: H. De Meyer
author: M. Van Daele
author: G. Vanden Berghe
reviewed by: Adrian Swift
MaRDI profile type: Publication
cites work: Q3779682
cites work: Comparing Numerical Methods for Ordinary Differential Equations
cites work: High order embedded Runge-Kutta formulae
cites work: Parallel iteration of high-order Runge-Kutta methods with stepsize control
cites work: Q5535370
full work available at URL: 0168-9274(93)90139-i
OpenAlex ID: W2143928122
description: scientific article; zbMATH DE number 459321