{"id":"https://openalex.org/W2022318891","doi":"https://doi.org/10.1016/j.cnsns.2013.05.022","title":"Wavelet operational matrix method for solving the Riccati differential equation","display_name":"Wavelet operational matrix method for solving the Riccati differential equation","publication_year":2013,"publication_date":"2013-08-23","ids":{"openalex":"https://openalex.org/W2022318891","doi":"https://doi.org/10.1016/j.cnsns.2013.05.022","mag":"2022318891"},"language":"en","primary_location":{"id":"doi:10.1016/j.cnsns.2013.05.022","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2013.05.022","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023576734","display_name":"Yuanlu Li","orcid":"https://orcid.org/0000-0003-3237-7235"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanlu Li","raw_affiliation_strings":["Assen (Nanjing) Environment Technology Co., Ltd., Nanjing 210042, China","School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Assen (Nanjing) Environment Technology Co., Ltd., Nanjing 210042, China","institution_ids":[]},{"raw_affiliation_string":"School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084704870","display_name":"Ning Sun","orcid":"https://orcid.org/0000-0002-5253-2944"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ning Sun","raw_affiliation_strings":["School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074697668","display_name":"Bo\u2010Chao Zheng","orcid":"https://orcid.org/0000-0001-6142-6580"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bochao Zheng","raw_affiliation_strings":["School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076700833","display_name":"Qi Wang","orcid":"https://orcid.org/0000-0003-3578-2551"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Wang","raw_affiliation_strings":["School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100649084","display_name":"Yingchao Zhang","orcid":"https://orcid.org/0000-0001-6225-4493"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingchao Zhang","raw_affiliation_strings":["School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023576734"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":{"value":3460,"currency":"USD","value_usd":3460},"apc_paid":null,"fwci":3.1963,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.90400591,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"3","first_page":"483","last_page":"493"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9890999794006348,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8234658241271973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7098035216331482},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6618088483810425},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.6283445954322815},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5736972689628601},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5223670601844788},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5177409052848816},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.42815518379211426},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41742292046546936},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35184288024902344},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.1870233714580536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1828702986240387},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.13656878471374512},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06174561381340027}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8234658241271973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7098035216331482},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6618088483810425},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.6283445954322815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5736972689628601},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5223670601844788},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5177409052848816},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.42815518379211426},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41742292046546936},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35184288024902344},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.1870233714580536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1828702986240387},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.13656878471374512},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06174561381340027},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cnsns.2013.05.022","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2013.05.022","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6659509694","display_name":null,"funder_award_id":"61271395","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8609368286","display_name":null,"funder_award_id":"2013M531387","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1517755115","https://openalex.org/W1965027360","https://openalex.org/W1966675876","https://openalex.org/W1968819460","https://openalex.org/W1969446688","https://openalex.org/W1976085526","https://openalex.org/W1983178975","https://openalex.org/W1984159491","https://openalex.org/W1988403512","https://openalex.org/W1991634374","https://openalex.org/W1996496941","https://openalex.org/W2000050774","https://openalex.org/W2004591828","https://openalex.org/W2013218122","https://openalex.org/W2013458971","https://openalex.org/W2017673835","https://openalex.org/W2021719174","https://openalex.org/W2026804296","https://openalex.org/W2029577600","https://openalex.org/W2030204179","https://openalex.org/W2039300886","https://openalex.org/W2045882715","https://openalex.org/W2048618474","https://openalex.org/W2049929235","https://openalex.org/W2059062496","https://openalex.org/W2061400438","https://openalex.org/W2061498519","https://openalex.org/W2068742490","https://openalex.org/W2079390764","https://openalex.org/W2080316206","https://openalex.org/W2086737859","https://openalex.org/W2088862817","https://openalex.org/W2089281733","https://openalex.org/W2089904505","https://openalex.org/W2094705180","https://openalex.org/W2101070138","https://openalex.org/W2106102602","https://openalex.org/W2134837756","https://openalex.org/W2165857509"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433","https://openalex.org/W2123585262","https://openalex.org/W2937301577"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}