Implementing an ODE code on distributed memory computers
type: Item
instance of: scholarly article
title: Implementing an ODE code on distributed memory computers
zbMATH Open document ID: 0810.65073
DOI: 10.1016/0898-1221(94)00194-4
publication date: 1995-04-09T00:00:00Z
review text: The Cauchy problem for a system of differential equations \(y'(t) = f(t, y(t))\), \(y(t_ 0) = y_ 0\) with \(f : [t_ 0, T] \times \mathbb{R}^ m \to \mathbb{R}^ m\) is studied. A continuous-time waveform relaxation method \[ z'{}^{(k + 1)} (t) = G(t, z^{(k + 1)} (t), y^{(n + 1)} (t), y^{(k+1)} (t), y^{(k)}(t)), \] \(z^{(k+1)} (t_ 0) = y_ 0\), \(y^{(0)} (t_ 0) = y_ 0\), \(y^{(k + 1)} (t) = g(t, z^{(k+1)} (t), y^{(t)} (t))\) is adapted for distributed memory parallel computers where \(G : [t_ 0, T] \times \mathbb{R}^{3m} \to \mathbb{R}^ m\), \(g: [t_ 0, T] \times \mathbb{R}^{2m} \to \mathbb{R}^ m\) satisfy \(G(t, y, y, y) = f(t, y)\), \(g(t, y, y) = f(t, y)\). An application to the diffusion Brusselator equation is given.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 699051
zbMATH Keywords: parallel computing
zbMATH Keywords: Cauchy problem
zbMATH Keywords: system
zbMATH Keywords: continuous-time waveform relaxation method
zbMATH Keywords: distributed memory parallel computers
zbMATH Keywords: diffusion Brusselator equation
author: Kevin Burrage
author: Bert Pohl
reviewed by: Miroslav Bartušek
describes a project that uses: DIFSUB
describes a project that uses: ODEPACK
describes a project that uses: PVM
describes a project that uses: LSODE
describes a project that uses: VODE
MaRDI profile type: Publication
full work available at URL: 0898-1221(94)00194-4
OpenAlex ID: W2084903644
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 699051