Validation of results of collocation methods for ODEs with CADNA library
type: Item
instance of: scholarly article
title: Validation of results of collocation methods for ODEs with CADNA library
zbMATH Open document ID: 0858.65084
DOI: 10.1016/0168-9274(96)00004-9
author: Yanyan Li
published in: Applied Numerical Mathematics
publication date: 1996-10-20T00:00:00Z
review text: This paper shows the efficiency of collocation methods for integrating systems of ordinary differential equations (ODEs) when they are performed with an efficient round-off error analysis method. The collocation methods are briefly presented and some of their properties are recalled. It is shown that they can be used as parallel across time methods. The CESTAC method for round-off error analysis, stochastic arithmetic and some of their properties are also recalled. Examples of linear and nonlinear initial values problems are solved with collocation methods. It is shown that collocation methods considered as parallel across time and performed with the CADNA library are efficient for solving ordinary differential equations.
reviewed by: F. Zhang
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 937358
zbMATH Keywords: result validation
zbMATH Keywords: parallel computation
zbMATH Keywords: error propagation
zbMATH Keywords: collocation methods
zbMATH Keywords: round-off error analysis
zbMATH Keywords: CESTAC method
zbMATH Keywords: stochastic arithmetic
zbMATH Keywords: CADNA library
MaRDI profile type: Publication
full work available at URL: 0168-9274(96)00004-9
OpenAlex ID: W2066494868
cites work: Accélération de la convergence en analyse numérique
cites work: Extrapolation methods theory and practice
cites work: Parallel methods for initial value problems
cites work: Q4725642
cites work: Diagonally-implicit multi-stage integration methods
cites work: Q3140942
cites work: Q3805775
cites work: Q4697161
cites work: Some Computer Organizations and Their Effectiveness
cites work: Parallel Solution of Ordinary Differential Equations
cites work: Q3821493
cites work: Q3357444
cites work: Parallelism across time in ODEs
cites work: Q3550030
cites work: On the Theory of Parallel Runge—Kutta Methods
cites work: Q5559978
cites work: Parallel Methods for the Numerical Integration of Ordinary Differential Equations
cites work: Q4721511
cites work: Block Implicit One-Step Methods
cites work: Parallel step-by-step methods
cites work: Iterated Runge–Kutta Methods on Parallel Computers
cites work: New methods for evaluating the validity of the results of mathematical computations
cites work: Q3743298
cites work: Review on stochastic approach to round-off error analysis and its applications
cites work: Q4727290
cites work: Q3915266
cites work: The Application of Implicit Runge-Kutta and Collocation Methods to Boundary-Value Problems
description: scientific article; zbMATH DE number 937358