{"id":"https://openalex.org/W2054662469","doi":"https://doi.org/10.1155/2012/241984","title":"On the Convergence of Continuous\u2010Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems","display_name":"On the Convergence of Continuous\u2010Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2054662469","doi":"https://doi.org/10.1155/2012/241984","mag":"2054662469"},"language":"en","primary_location":{"id":"doi:10.1155/2012/241984","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/241984","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/241984.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/2012/241984.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055408340","display_name":"Yongxiang Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]},{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongxiang Zhao","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, Xiangtan, China","School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China","Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, Xiangtan","School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000"],"affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, Xiangtan, China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China","institution_ids":["https://openalex.org/I50180762"]},{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, Xiangtan","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000","institution_ids":["https://openalex.org/I50180762"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100361116","display_name":"Li Li","orcid":"https://orcid.org/0000-0002-1925-3169"},"institutions":[{"id":"https://openalex.org/I50180762","display_name":"Chongqing Three Gorges University","ror":"https://ror.org/05rs3pv16","country_code":"CN","type":"education","lineage":["https://openalex.org/I50180762"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Li","raw_affiliation_strings":["School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China","School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China","institution_ids":["https://openalex.org/I50180762"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000","institution_ids":["https://openalex.org/I50180762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055408340"],"corresponding_institution_ids":["https://openalex.org/I4610292","https://openalex.org/I50180762"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.4483,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6459854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9907000064849854,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7884470224380493},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.7019271850585938},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.6351744532585144},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6244776248931885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6195886135101318},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5238473415374756},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5238242745399475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48070961236953735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4690416753292084},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32732510566711426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1879597008228302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1577620506286621}],"concepts":[{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7884470224380493},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.7019271850585938},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.6351744532585144},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6244776248931885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6195886135101318},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5238473415374756},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5238242745399475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48070961236953735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4690416753292084},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32732510566711426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1879597008228302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1577620506286621},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/241984","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/241984","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/241984.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/1355495241","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495241","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:241984","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/241984.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:519c8f8742d247659a47442982d3dcc3","is_oa":true,"landing_page_url":"https://doaj.org/article/519c8f8742d247659a47442982d3dcc3","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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:10.1155/2012/241984","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/241984","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/241984.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":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1219020495","display_name":null,"funder_award_id":"10971175","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G1283578889","display_name":null,"funder_award_id":"11126329","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G1409938592","display_name":null,"funder_award_id":"20094301110001","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3578167484","display_name":null,"funder_award_id":"10971175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G422832145","display_name":null,"funder_award_id":"09JJ3002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4520930998","display_name":null,"funder_award_id":"20094301110001","funder_id":"https://openalex.org/F4320336024","funder_display_name":"Specialized Research Fund for the Doctoral Program of Higher Education of China"},{"id":"https://openalex.org/G5087429297","display_name":null,"funder_award_id":"KJ121110","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G5565435882","display_name":null,"funder_award_id":"20094301110001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5741814991","display_name":null,"funder_award_id":"11126329","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5760752404","display_name":null,"funder_award_id":"Projects","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6918464587","display_name":null,"funder_award_id":"09JJ3002","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G790037715","display_name":null,"funder_award_id":"KJ121110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8650761135","display_name":"Genetic Dissection of the Specificity of Leucine Zipper Dimerization","funder_award_id":"0111000","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8882644488","display_name":"Enabling precision calibration of massively multiplexed spectroscopic surveys","funder_award_id":"2009430","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322866","display_name":"Natural Science Foundation of Hainan Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336024","display_name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054662469.pdf","grobid_xml":"https://content.openalex.org/works/W2054662469.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W126013857","https://openalex.org/W1511461612","https://openalex.org/W1524707262","https://openalex.org/W1972061314","https://openalex.org/W1980309222","https://openalex.org/W1986792623","https://openalex.org/W2006232635","https://openalex.org/W2007665571","https://openalex.org/W2032428933","https://openalex.org/W2036597275","https://openalex.org/W2052312612","https://openalex.org/W2070673846","https://openalex.org/W2090990151","https://openalex.org/W2138117444","https://openalex.org/W4252247111"],"related_works":["https://openalex.org/W2163370649","https://openalex.org/W4327639758","https://openalex.org/W1998082046","https://openalex.org/W2116787190","https://openalex.org/W2154304710","https://openalex.org/W2019676381","https://openalex.org/W1982149897","https://openalex.org/W2387468633","https://openalex.org/W2006371715","https://openalex.org/W2713536231"],"abstract_inverted_index":{"This":[0],"paper":[1],"extends":[2],"the":[3],"continuous\u2010time":[4,20],"waveform":[5,21],"relaxation":[6,22],"method":[7],"to":[8],"singular":[9,25],"perturbation":[10,26],"initial":[11,27],"value":[12,28],"problems.":[13],"The":[14],"sufficient":[15],"conditions":[16],"for":[17,24],"convergence":[18],"of":[19],"methods":[23],"problems":[29],"are":[30],"given.":[31]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2016-06-24T00:00:00"}