Discretization of implicit ODEs for singular root-finding problems
type: Item
instance of: scholarly article
title: Discretization of implicit ODEs for singular root-finding problems
zbMATH Open document ID: 1001.65050
DOI: 10.1016/S0377-0427(01)00404-6
author: Ricardo Riaza
author: Pedro J. Zufiria
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The iteration generated by the numerical integration of an ordinary differential equation (ODE) may be studied as a discrete dynamical system. Starting from this fact, the paper considers different discretizations of continuous-time models for singular root-finding and optimization problems. The paper is devoted, firstly, to the use of discrete-time analysis techniques for singular problems, based on continuous-time stability and numerical stability and, secondly, to introduce a systematic methodology for the formulation of quadratically convergent iterations for singular root-finding problems.
reviewed by: Vasile Berinde
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 1758454
zbMATH Keywords: continuous-time model
zbMATH Keywords: quadratic convergence
zbMATH Keywords: iterative method
zbMATH Keywords: discrete dynamical system
zbMATH Keywords: explicit Runge-Kutta methods
zbMATH Keywords: continuous Newton method
zbMATH Keywords: singular root-finding
zbMATH Keywords: optimization
zbMATH Keywords: discrete-time analysis
zbMATH Keywords: continuous-time stability
zbMATH Keywords: numerical stability
describes a project that uses: HOMPACK90
describes a project that uses: RODAS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758454