Periodic waveform relaxation solutions of nonlinear dynamic equations.
type: Item
instance of: scholarly article
title: Periodic waveform relaxation solutions of nonlinear dynamic equations.
zbMATH Open document ID: 1088.34520
DOI: 10.1016/S0096-3003(01)00324-1
author: Yao-Lin Jiang
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Consider the periodic system \[ \frac{dx}{dt}=f(x,t)\tag{*} \] in \(\mathbb{R}^n\), where \(f\) is \(T\)-periodic in \(t\). Let \(F(x,y,y)\) be a splitting of \(f\), that is \(f(x,t) \equiv F(x,x,t)\). To compute a \(T\)-periodic solution of (*), the author uses the iteration schema \[ \frac{dx^{k+1}}{dt}= F\bigl (x^t(t),x^{k+1},t\bigr),\;x^{k+1} (0)=x^{k+1}(T),\tag{**} \] known as waveform iteration. The author provides a sufficient condition for the convergence of (**). The conditions obtained are known in the theory of waveform iteration.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 1861339
reviewed by: Klaus R. Schneider
describes a project that uses: Global Optimization Toolbox For Maple
MaRDI profile type: Publication
cites work: Q3841797
cites work: Q3997058
cites work: Q4109220
cites work: Monotone Waveform Relaxation for Systems of Nonlinear Differential-Algebraic Equations
cites work: A note on convergence conditions of waveform relaxation algorithms for nonlinear differential-algebraic equations
cites work: On Dynamic Iteration Methods for Solving Time-Periodic Differential Equations
cites work: Q4325928
full work available at URL: s0096-3003(01)00324-1
OpenAlex ID: W2090640823
description: scientific article; zbMATH DE number 1861339