{"id":"https://openalex.org/W2022382654","doi":"https://doi.org/10.1137/s0036142903421278","title":"Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains","display_name":"Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2022382654","doi":"https://doi.org/10.1137/s0036142903421278","mag":"2022382654"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903421278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903421278","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":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/hermite-spectral-methods-with-a-time-dependent-scaling-for-parabo","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087806562","display_name":"Heping Ma","orcid":"https://orcid.org/0000-0002-8891-7635"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heping Ma","raw_affiliation_strings":["Shanghai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai University","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014226512","display_name":"Weiwei Sun","orcid":"https://orcid.org/0000-0002-2079-4480"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Weiwei Sun","raw_affiliation_strings":["City University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058967726","display_name":"Tao Tang","orcid":"https://orcid.org/0000-0003-2919-2774"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Tang","raw_affiliation_strings":["Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0462,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.85975799,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"43","issue":"1","first_page":"58","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9993000030517578,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.8497684597969055},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.7847625017166138},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5662195086479187},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5643543004989624},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49531593918800354},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.48711180686950684},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.4705864489078522},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45306310057640076},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44164878129959106},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41283273696899414},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10844892263412476}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8497684597969055},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7847625017166138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5662195086479187},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5643543004989624},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49531593918800354},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.48711180686950684},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.4705864489078522},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45306310057640076},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44164878129959106},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41283273696899414},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10844892263412476},{"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036142903421278","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903421278","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/hermite-spectral-methods-with-a-time-dependent-scaling-for-parabo","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"},{"id":"pmh:oai:pure.atira.dk:publications/71777520-3662-4b59-80e3-ab426cf39263","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/71777520-3662-4b59-80e3-ab426cf39263","pdf_url":"https://scholars.cityu.edu.hk/files/189049387/5191941.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ma, H, Sun, W & Tang, T 2005, 'Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains', SIAM Journal on Numerical Analysis, vol. 43, no. 1, pp. 58-75. https://doi.org/10.1137/S0036142903421278","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.493.3473","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.493.3473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hkbu.edu.hk/~ttang/Papers/4-42127.pdf","raw_type":"text"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/hermite-spectral-methods-with-a-time-dependent-scaling-for-parabo","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"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W166141713","https://openalex.org/W1483324267","https://openalex.org/W1599524282","https://openalex.org/W1968563346","https://openalex.org/W1971743999","https://openalex.org/W1972266929","https://openalex.org/W1975666830","https://openalex.org/W1976760067","https://openalex.org/W1985849492","https://openalex.org/W2000100391","https://openalex.org/W2007254031","https://openalex.org/W2007997432","https://openalex.org/W2013282326","https://openalex.org/W2024923766","https://openalex.org/W2065002736","https://openalex.org/W2065378774","https://openalex.org/W2065522541","https://openalex.org/W2072022733","https://openalex.org/W2072653497","https://openalex.org/W2078959912","https://openalex.org/W2094866248","https://openalex.org/W2129992549","https://openalex.org/W2169070947","https://openalex.org/W2992211051","https://openalex.org/W3036926079","https://openalex.org/W4213061483","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4376866960","https://openalex.org/W1697484951","https://openalex.org/W4297084911","https://openalex.org/W1992244398","https://openalex.org/W2362641799","https://openalex.org/W4298930346","https://openalex.org/W4226238329","https://openalex.org/W4361230184","https://openalex.org/W3166395799","https://openalex.org/W1494666726"],"abstract_inverted_index":{"Hermite":[0,34,50,139],"spectral":[1,35,63,140],"methods":[2,36],"are":[3,101,144],"investigated":[4],"for":[5,68],"linear":[6],"diffusion":[7,23],"equations":[8,12],"and":[9,62,89,110,152],"nonlinear":[10],"convection-diffusion":[11],"in":[13,48,78],"unbounded":[14],"domains.":[15],"When":[16],"the":[17,22,33,49,79,82,104,118,121,127,134,149],"solution":[18],"domain":[19],"is":[20,46,107,111,125],"unbounded,":[21],"operator":[24],"no":[25],"longer":[26],"has":[27],"a":[28,42,54,59,75],"compact":[29],"resolvent,":[30],"which":[31,52],"makes":[32],"unstable.":[37],"To":[38],"overcome":[39],"this":[40,69],"difficulty,":[41],"time-dependent":[43,119],"scaling":[44,120],"factor":[45],"employed":[47],"expansions,":[51],"yields":[53],"positive":[55],"bilinear":[56],"form.":[57],"As":[58],"consequence,":[60],"stability":[61,80,151],"convergence":[64,153],"can":[65],"be":[66],"established":[67],"approach.":[70],"The":[71],"present":[72,105],"method":[73],"plays":[74],"similar":[76],"role":[77],"of":[81,126],"{similarity":[83],"transformation}":[84],"technique":[85],"proposed":[86],"by":[87],"Funaro":[88],"Kavian":[90],"[Math.":[91],"Comp.,":[92],"57":[93],"(1991),":[94],"pp.":[95],"597--619].":[96],"However,":[97],"since":[98],"coordinate":[99],"transformations":[100],"not":[102],"required,":[103],"approach":[106],"more":[108],"efficient":[109],"easier":[112],"to":[113,147],"implement.":[114],"In":[115],"fact,":[116],"with":[117,133],"resulting":[122],"discretization":[123],"system":[124],"same":[128],"form":[129],"as":[130],"that":[131],"associated":[132],"classical":[135],"(straightforward":[136],"but":[137],"unstable)":[138],"method.":[141],"Numerical":[142],"experiments":[143],"carried":[145],"out":[146],"support":[148],"theoretical":[150],"results.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}