Numerical differentiation of implicitly defined curves
type: Item
instance of: scholarly article
title: Numerical differentiation of implicitly defined curves
zbMATH Open document ID: 0939.65029
DOI: 10.1016/S0377-0427(99)00106-5
author: Muhammed Syam
author: Hani I. Siyyam
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-10T00:00:00Z
review text: In the context of numerical continuation methods, one considers curves which are implicitly defined by an undetermined system of equations \(H(u)= 0\) where \(H: \mathbb{R}^{n+1}\to \mathbb{R}^n\) is a smooth map. The authors develop a finite differencing device to calculate approximations of derivatives \(c'(0),c''(0),\dots\) of regular solution curves \(c: \mathbb{R}\ni s\to c(s)\in \mathbb{R}^n\) of systems of nonlinear equations \(f(x)= 0\), \(f\in C^k(\mathbb{R}^{n+ 1},\mathbb{R}^n)\) without having to compute points on the solution curve \(c(s)\). The derivative vectors \(c'(0),c''(0),\dots\) can be used in the numerical approximation of the solution set \(f^{-1}(0)\) to construct higher-order predictors to be used in the predictor-corrector continuation method.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 1367894
zbMATH Keywords: numerical differentiation
zbMATH Keywords: approximations of derivatives
zbMATH Keywords: redictor-corrector continuation method
MaRDI profile type: Publication
cites work: Q3998344
cites work: Q3139554
cites work: Numerical differentiation of implicitly defined space curves
Wikidata QID: Q126550706
full work available at URL: s0377-0427(99)00106-5
OpenAlex ID: W2085484341
description: scientific article; zbMATH DE number 1367894