{"id":"https://openalex.org/W2073777570","doi":"https://doi.org/10.1137/090773581","title":"Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains","display_name":"Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2073777570","doi":"https://doi.org/10.1137/090773581","mag":"2073777570"},"language":"en","primary_location":{"id":"doi:10.1137/090773581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090773581","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5102082914","display_name":"Xin-min Xiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xin-min Xiang","raw_affiliation_strings":["xiangxm@shnu.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"xiangxm@shnu.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100369600","display_name":"Zhongqing Wang","orcid":"https://orcid.org/0000-0002-3281-5322"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong-qing Wang","raw_affiliation_strings":["zqwang@shnu.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"zqwang@shnu.edu.cn#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102082914"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5731,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.81618037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"48","issue":"4","first_page":"1231","last_page":"1253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8582747578620911},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.8363503813743591},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6026228070259094},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5912761688232422},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49142706394195557},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"Spectral analysis","score":0.482216477394104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43304187059402466},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4148308038711548}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8582747578620911},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8363503813743591},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6026228070259094},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5912761688232422},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49142706394195557},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.482216477394104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43304187059402466},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4148308038711548},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C32891209","wikidata":"https://www.wikidata.org/wiki/Q483666","display_name":"Spectroscopy","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090773581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090773581","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W560409768","https://openalex.org/W1549220217","https://openalex.org/W1968300725","https://openalex.org/W1975666830","https://openalex.org/W1978022759","https://openalex.org/W1985849492","https://openalex.org/W1995255204","https://openalex.org/W2000100391","https://openalex.org/W2013282326","https://openalex.org/W2022382654","https://openalex.org/W2028522134","https://openalex.org/W2078959912","https://openalex.org/W2090496377","https://openalex.org/W2092280105","https://openalex.org/W2094866248","https://openalex.org/W2133304313","https://openalex.org/W2152014006","https://openalex.org/W2346165189"],"related_works":["https://openalex.org/W4383100562","https://openalex.org/W175020571","https://openalex.org/W1965919058","https://openalex.org/W1628946225","https://openalex.org/W2323905825","https://openalex.org/W4294204420","https://openalex.org/W2952295687","https://openalex.org/W4256575470","https://openalex.org/W1978605241","https://openalex.org/W2504888288"],"abstract_inverted_index":{"In":[0],"this":[1,72],"paper,":[2],"we":[3],"develop":[4],"a":[5,42,50],"spectral":[6,33,56,69],"method":[7],"based":[8],"on":[9,22],"generalized":[10,23,38],"Hermite":[11,24],"functions":[12],"with":[13,49],"weight":[14],"$\\chi(x)\\equiv1$.":[15],"We":[16],"also":[17],"establish":[18],"some":[19],"basic":[20],"results":[21,66],"orthogonal":[25],"approximations,":[26],"which":[27],"play":[28],"an":[29,46],"important":[30],"role":[31],"in":[32,41],"methods.":[34],"As":[35],"examples,":[36],"the":[37,68],"Ginzburg\u2013Landau":[39],"equation":[40,48],"population":[43],"problem":[44],"and":[45,60],"elliptic":[47],"harmonic":[51],"potential":[52],"are":[53,58],"considered.":[54],"Related":[55],"schemes":[57],"proposed,":[59],"their":[61],"convergence":[62],"is":[63],"proved.":[64],"Numerical":[65],"demonstrate":[67],"accuracy":[70],"of":[71],"approach.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}