On higher-order differentiation in nonlinear mechanics

Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymp...

Full description

Saved in:
Bibliographic Details
Published in:Optimization methods & software 2012-04, Vol.27 (2), p.221-232
Main Author: Charpentier, I.
Format: Article
Language:English
Subjects:
74-02
asymptotic methods
automatic differentiation
bifurcation analysis
Diamant
Mechanics
Methods
nonlinear problems
Numerical analysis
Studies
Taylor series
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943
cites cdi_FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943
container_end_page 232
container_issue 2
container_start_page 221
container_title Optimization methods & software
container_volume 27
creator Charpentier, I.
description Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.
doi_str_mv 10.1080/10556788.2011.577775
format article
fullrecord <record><control><sourceid>proquest_infor</sourceid><recordid>TN_cdi_proquest_journals_1151451615</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2814340181</sourcerecordid><originalsourceid>FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKv_wMOC561JNrPZPYkUv6DQi55DNh82ZZvUyRbpv3fL6tW5zBye9x14CLlldMFoQ-8ZBahl0yw4ZWwBchw4IzNGeVuKtpLnpxugPDGX5CrnLaVUMFHPSL2OxSZ8bhyWCa3DwgbvHbo4BD2EFIsQi5hiH6LTWOyc2egYTL4mF1732d387jn5eH56X76Wq_XL2_JxVZqqgqHknHaubsBoWxljW2u9Aaldw4XjnNedMN5QkB1IV3FZg-HSSDuGOZddK6o5uZt695i-Di4PapsOGMeXijFgAljNYKTERBlMOaPzao9hp_GoGFUnQ-rPkDoZUpOhMfYwxUL0CXf6O2Fv1aCPfUKPOpqQVfVvww-l4mw9</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1151451615</pqid></control><display><type>article</type><title>On higher-order differentiation in nonlinear mechanics</title><source>Taylor and Francis Science and Technology Collection</source><creator>Charpentier, I.</creator><creatorcontrib>Charpentier, I.</creatorcontrib><description>Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.</description><identifier>ISSN: 1055-6788</identifier><identifier>EISSN: 1029-4937</identifier><identifier>DOI: 10.1080/10556788.2011.577775</identifier><language>eng</language><publisher>Abingdon: Taylor &amp; Francis</publisher><subject>74-02 ; asymptotic methods ; automatic differentiation ; bifurcation analysis ; Diamant ; Mechanics ; Methods ; nonlinear problems ; Numerical analysis ; Studies ; Taylor series</subject><ispartof>Optimization methods &amp; software, 2012-04, Vol.27 (2), p.221-232</ispartof><rights>Copyright Taylor &amp; Francis Group, LLC 2012</rights><rights>Copyright Taylor and Francis Group, LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943</citedby><cites>FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Charpentier, I.</creatorcontrib><title>On higher-order differentiation in nonlinear mechanics</title><title>Optimization methods &amp; software</title><description>Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.</description><subject>74-02</subject><subject>asymptotic methods</subject><subject>automatic differentiation</subject><subject>bifurcation analysis</subject><subject>Diamant</subject><subject>Mechanics</subject><subject>Methods</subject><subject>nonlinear problems</subject><subject>Numerical analysis</subject><subject>Studies</subject><subject>Taylor series</subject><issn>1055-6788</issn><issn>1029-4937</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKv_wMOC561JNrPZPYkUv6DQi55DNh82ZZvUyRbpv3fL6tW5zBye9x14CLlldMFoQ-8ZBahl0yw4ZWwBchw4IzNGeVuKtpLnpxugPDGX5CrnLaVUMFHPSL2OxSZ8bhyWCa3DwgbvHbo4BD2EFIsQi5hiH6LTWOyc2egYTL4mF1732d387jn5eH56X76Wq_XL2_JxVZqqgqHknHaubsBoWxljW2u9Aaldw4XjnNedMN5QkB1IV3FZg-HSSDuGOZddK6o5uZt695i-Di4PapsOGMeXijFgAljNYKTERBlMOaPzao9hp_GoGFUnQ-rPkDoZUpOhMfYwxUL0CXf6O2Fv1aCPfUKPOpqQVfVvww-l4mw9</recordid><startdate>20120401</startdate><enddate>20120401</enddate><creator>Charpentier, I.</creator><general>Taylor &amp; Francis</general><general>Taylor &amp; Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20120401</creationdate><title>On higher-order differentiation in nonlinear mechanics</title><author>Charpentier, I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>74-02</topic><topic>asymptotic methods</topic><topic>automatic differentiation</topic><topic>bifurcation analysis</topic><topic>Diamant</topic><topic>Mechanics</topic><topic>Methods</topic><topic>nonlinear problems</topic><topic>Numerical analysis</topic><topic>Studies</topic><topic>Taylor series</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Charpentier, I.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Optimization methods &amp; software</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Charpentier, I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On higher-order differentiation in nonlinear mechanics</atitle><jtitle>Optimization methods &amp; software</jtitle><date>2012-04-01</date><risdate>2012</risdate><volume>27</volume><issue>2</issue><spage>221</spage><epage>232</epage><pages>221-232</pages><issn>1055-6788</issn><eissn>1029-4937</eissn><abstract>Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.</abstract><cop>Abingdon</cop><pub>Taylor &amp; Francis</pub><doi>10.1080/10556788.2011.577775</doi><tpages>12</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1055-6788
ispartof Optimization methods & software, 2012-04, Vol.27 (2), p.221-232
issn 1055-6788
1029-4937
language eng
recordid cdi_proquest_journals_1151451615
source Taylor and Francis Science and Technology Collection
subjects 74-02
asymptotic methods
automatic differentiation
bifurcation analysis
Diamant
Mechanics
Methods
nonlinear problems
Numerical analysis
Studies
Taylor series
title On higher-order differentiation in nonlinear mechanics
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T21%3A26%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_infor&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20higher-order%20differentiation%20in%20nonlinear%20mechanics&rft.jtitle=Optimization%20methods%20&%20software&rft.au=Charpentier,%20I.&rft.date=2012-04-01&rft.volume=27&rft.issue=2&rft.spage=221&rft.epage=232&rft.pages=221-232&rft.issn=1055-6788&rft.eissn=1029-4937&rft_id=info:doi/10.1080/10556788.2011.577775&rft_dat=%3Cproquest_infor%3E2814340181%3C/proquest_infor%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c335t-220be685cad3ccd9ddfc57ae824e2226b4cfc057b57e32765c27c7dc33227b943%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1151451615&rft_id=info:pmid/&rfr_iscdi=true