Convergence aspects of step-parallel iteration of Runge-Kutta methods
type: Item
instance of: scholarly article
title: Convergence aspects of step-parallel iteration of Runge-Kutta methods
zbMATH Open document ID: 0837.65076
DOI: 10.1016/0168-9274(95)00063-Z
author: W. A. van der Veen
author: P. J. van der Houwen
author: Jacques J. B. de Swart
published in: Applied Numerical Mathematics
publication date: 1996-01-07T00:00:00Z
review text: 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.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 815835
zbMATH Keywords: parallel computation
zbMATH Keywords: parallelism across steps
zbMATH Keywords: implicit Runge-Kutta methods
zbMATH Keywords: Radau IIA
zbMATH Keywords: convergence
zbMATH Keywords: test equation
zbMATH Keywords: iteration methods
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Q3830493
cites work: Parallel ODE-solvers with stepsize control
cites work: Q4725642
cites work: Q4000061
cites work: The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
cites work: Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
cites work: Q5604166
cites work: Iterated Runge–Kutta Methods on Parallel Computers
cites work: Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems
cites work: Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems
cites work: Step-parallel algorithms for stiff initial value problems
full work available at URL: 0168-9274(95)00063-z
OpenAlex ID: W2142448970
description: scientific article; zbMATH DE number 815835