{"id":"https://openalex.org/W2071373094","doi":"https://doi.org/10.1155/2012/906341","title":"An Optimal Iteration Method for Strongly Nonlinear Oscillators","display_name":"An Optimal Iteration Method for Strongly Nonlinear Oscillators","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2071373094","doi":"https://doi.org/10.1155/2012/906341","mag":"2071373094"},"language":"en","primary_location":{"id":"doi:10.1155/2012/906341","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/906341","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/906341.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/906341.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042875545","display_name":"Vasile Marinca","orcid":"https://orcid.org/0000-0002-0947-1322"},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Vasile Marinca","raw_affiliation_strings":["Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara, Romania","Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara, Romania","Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara","Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara"],"affiliations":[{"raw_affiliation_string":"Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara, Romania","institution_ids":["https://openalex.org/I3122695212"]},{"raw_affiliation_string":"Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara","institution_ids":["https://openalex.org/I3122695212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012096611","display_name":"Nicolae Heri\u015fanu","orcid":"https://orcid.org/0000-0003-2968-5309"},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Nicolae Heri\u015fanu","raw_affiliation_strings":["Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara","Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara"],"affiliations":[{"raw_affiliation_string":"Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara","institution_ids":["https://openalex.org/I3122695212"]},{"raw_affiliation_string":"Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012096611"],"corresponding_institution_ids":["https://openalex.org/I3122695212","https://openalex.org/I58077936"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.0468,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.75059076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.7298660278320312},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6597582101821899},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6487739086151123},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6242834329605103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5715442895889282},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5105055570602417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3484853506088257},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32281529903411865},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2742008566856384},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11035388708114624},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08154433965682983}],"concepts":[{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7298660278320312},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6597582101821899},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6487739086151123},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6242834329605103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5715442895889282},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5105055570602417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3484853506088257},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32281529903411865},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2742008566856384},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11035388708114624},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08154433965682983},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/906341","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/906341","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/906341.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1350479409","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1350479409","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:906341","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/906341.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:3ca23bf3b18a42da96add91da1bc10e3","is_oa":true,"landing_page_url":"https://doaj.org/article/3ca23bf3b18a42da96add91da1bc10e3","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/906341","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/906341","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/906341.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071373094.pdf","grobid_xml":"https://content.openalex.org/works/W2071373094.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W187465303","https://openalex.org/W581313666","https://openalex.org/W1690786936","https://openalex.org/W1970992650","https://openalex.org/W1986885854","https://openalex.org/W1990353179","https://openalex.org/W1999443364","https://openalex.org/W2002275289","https://openalex.org/W2009009950","https://openalex.org/W2044369117","https://openalex.org/W2062712646","https://openalex.org/W2070287549","https://openalex.org/W2159676772","https://openalex.org/W2165917005","https://openalex.org/W2949840325","https://openalex.org/W4231409469","https://openalex.org/W4235488236"],"related_works":["https://openalex.org/W2553468687","https://openalex.org/W2953137247","https://openalex.org/W2362574016","https://openalex.org/W2666785071","https://openalex.org/W2059396883","https://openalex.org/W130230158","https://openalex.org/W4388093135","https://openalex.org/W2999135108","https://openalex.org/W2363340714","https://openalex.org/W2119556180"],"abstract_inverted_index":{"We":[0,25],"introduce":[1],"a":[2,69,80],"new":[3],"method,":[4],"namely,":[5],"the":[6,56,74],"Optimal":[7],"Iteration":[8],"Perturbation":[9],"Method":[10],"(OIPM),":[11],"to":[12,43,52,72],"solve":[13],"nonlinear":[14],"differential":[15],"equations":[16],"of":[17,55,61,76,87],"oscillators":[18],"with":[19],"cubic":[20],"and":[21,32,34,84,100,110],"harmonic":[22],"restoring":[23],"force.":[24],"illustrate":[26],"that":[27,66,105],"OIPM":[28,106],"is":[29,107],"very":[30,81,93,108],"effective":[31],"convenient":[33,70],"does":[35],"not":[36],"require":[37],"linearization":[38],"or":[39],"small":[40],"perturbation.":[41],"Contrary":[42],"conventional":[44],"methods,":[45],"in":[46,65,79],"OIPM,":[47],"only":[48],"one":[49],"iteration":[50],"leads":[51],"high":[53],"accuracy":[54],"solutions.":[57],"The":[58],"main":[59],"advantage":[60],"this":[62],"approach":[63],"consists":[64],"it":[67],"provides":[68],"way":[71,83],"control":[73],"convergence":[75,88],"approximate":[77,99],"solutions":[78],"rigorous":[82],"allows":[85],"adjustment":[86],"regions":[89],"where":[90],"necessary.":[91],"A":[92],"good":[94],"agreement":[95],"was":[96],"found":[97],"between":[98],"numerical":[101],"solutions,":[102],"which":[103],"prove":[104],"efficient":[109],"accurate.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
