A new iterative numerical continuation technique for approximating the solutions of scalar nonlinear equations
type: Item
instance of: scholarly article
title: A new iterative numerical continuation technique for approximating the solutions of scalar nonlinear equations
zbMATH Open document ID: 1413.65180
DOI: 10.1155/2017/2783682
author: Grégory Antoni
published in: International Journal of Engineering Mathematics
publication date: 2018-08-06T00:00:00Z
review text: Summary: The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton's technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6913876
Wikidata QID: Q59144368
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/2783682
OpenAlex ID: W2576261777
cites work: Q4499064
cites work: Q4519745
cites work: Nonlinear finite element analysis of solids and structures
cites work: Solving Nonlinear Equations with Newton's Method
cites work: Q4498398
cites work: A new accurate and efficient iterative numerical method for solving the scalar and vector nonlinear equations: approach based on geometric considerations
cites work: An efficient and straightforward numerical technique coupled to classical Newton's method for enhancing the accuracy of approximate solutions associated with scalar nonlinear equations
cites work: A fast incremental/iterative solution procedure that handles “snap-through”
cites work: An arc-length method including line searches and accelerations
cites work: The Application of Newton’s Method to the Problem of Elastic Stability
cites work: An incremental approach to the solution of snapping and buckling problems
cites work: Some computational aspects of the stability analysis of nonlinear structures
cites work: Q3929130
cites work: Q3327983
cites work: Discrete approximations related to nonlinear theories of solids
cites work: A comparison of three algorithms for tracing nonlinear equilibrium paths of structural systems
description: scientific article; zbMATH DE number 6913876