Convergence results for continuous-time waveform methods for Volterra integral equations
type: Item
instance of: scholarly article
title: Convergence results for continuous-time waveform methods for Volterra integral equations
zbMATH Open document ID: 0855.65142
DOI: 10.1016/0377-0427(95)00225-1
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 1997-02-11T00:00:00Z
review text: The paper deals with iterative methods (the waveform relaxation (WR) methods) for solving systems of second kind Volterra integral equations. A different approach to the parallelism, the parallelism ``across space'', is considered and continuous-time waveform relaxation methods are also investigated. Many particular methods (Picard method, Jacobi method, Gauss-Seidel method, Newton method, Richardson method) are discussed from the point of view of their convergence properties. Particular attention is devoted to parallel WR methods, since they are particularly suitable in solving large systems of Volterra integral equations.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 910301
zbMATH Keywords: parallel computing
zbMATH Keywords: Picard method
zbMATH Keywords: iterative methods
zbMATH Keywords: waveform relaxation methods
zbMATH Keywords: systems of second kind Volterra integral equations
zbMATH Keywords: Jacobi method
zbMATH Keywords: Gauss-Seidel method
zbMATH Keywords: Newton method
zbMATH Keywords: Richardson method
zbMATH Keywords: convergence
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00225-1
OpenAlex ID: W2006232635
cites work: Q3213489
cites work: Stability of parallel Volterra-Runge-Kutta methods
cites work: Thresholds and travelling waves for the geographical spread of infection
cites work: A class of parallel \(V_0\)-stable methods for Volterra integral equations
cites work: Waveform methods for space and time parallelism
cites work: Continuous time collocation methods for Volterra-Fredholm integral equations
cites work: Convergence of Dynamic Iteration Methods for Initial Value Problems
cites work: Remarks on Picard-Lindelöf iteration
cites work: Q4275382
Recommended article: Continuous and discrete time waveform relaxation methods for Volterra integral equations with weakly singular kernels
Recommended article: Q5319785
Recommended article: On the convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems
Recommended article: Q3579657
Recommended article: Discrete-time waveform relaxation Volterra-Runge-Kutta methods: Convergence analysis
Recommended article: A parallel fast convergent waveform relaxation method for Volterra integral equations.
Recommended article: Convergence of approximate solution of delay Volterra integral equations
Recommended article: Convergence analysis of discretization methods for nonlinear first kind Volterra integral equations
Recommended article: Convergence of multistep methods for Volterra integro-differential equations
Recommended article: Convergence analysis for delay Volterra integral equation
description: scientific article; zbMATH DE number 910301