{"id":"https://openalex.org/W2185021247","doi":"https://doi.org/10.1080/00207160.2015.1083555","title":"Optimal error bound and a quasi-boundary value regularization method for a Cauchy problem of the modified Helmholtz equation","display_name":"Optimal error bound and a quasi-boundary value regularization method for a Cauchy problem of the modified Helmholtz equation","publication_year":2015,"publication_date":"2015-08-18","ids":{"openalex":"https://openalex.org/W2185021247","doi":"https://doi.org/10.1080/00207160.2015.1083555","mag":"2185021247"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1083555","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1083555","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5075124454","display_name":"Ailin Qian","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101555","display_name":"Hubei University of Science and Technology","ror":"https://ror.org/018wg9441","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101555"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ailin Qian","raw_affiliation_strings":["School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei 437100, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei 437100, China","institution_ids":["https://openalex.org/I4210101555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101567758","display_name":"Xiaomei Yang","orcid":"https://orcid.org/0009-0009-4199-5212"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaomei Yang","raw_affiliation_strings":["School of Mathematical Sciences, Southwest Jiaotong University, Chengdu, Sichuang 610031, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Southwest Jiaotong University, Chengdu, Sichuang 610031, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114249096","display_name":"Yousheng Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101555","display_name":"Hubei University of Science and Technology","ror":"https://ror.org/018wg9441","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101555"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yousheng Wu","raw_affiliation_strings":["School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei 437100, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei 437100, China","institution_ids":["https://openalex.org/I4210101555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075124454"],"corresponding_institution_ids":["https://openalex.org/I4210101555"],"apc_list":null,"apc_paid":null,"fwci":0.5142,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65328766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"93","issue":"12","first_page":"2028","last_page":"2041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8283016085624695},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.79634690284729},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7099893689155579},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6926041841506958},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.619191586971283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.551966667175293},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5443397164344788},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.5354243516921997},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.47207120060920715},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44986677169799805},{"id":"https://openalex.org/keywords/cauchy-boundary-condition","display_name":"Cauchy boundary condition","score":0.44551894068717957},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.20520877838134766},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10963371396064758},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0721905529499054}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8283016085624695},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.79634690284729},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7099893689155579},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6926041841506958},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.619191586971283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.551966667175293},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5443397164344788},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.5354243516921997},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.47207120060920715},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44986677169799805},{"id":"https://openalex.org/C106947605","wikidata":"https://www.wikidata.org/wiki/Q3278575","display_name":"Cauchy boundary condition","level":4,"score":0.44551894068717957},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.20520877838134766},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10963371396064758},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0721905529499054},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1083555","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1083555","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1523113578","https://openalex.org/W1570089119","https://openalex.org/W1965790396","https://openalex.org/W1976537058","https://openalex.org/W1997740065","https://openalex.org/W2010184596","https://openalex.org/W2033914750","https://openalex.org/W2041249013","https://openalex.org/W2060506252","https://openalex.org/W2065565241","https://openalex.org/W2068414394","https://openalex.org/W2089816835","https://openalex.org/W2096715107","https://openalex.org/W2100219897","https://openalex.org/W2134154463","https://openalex.org/W4292027041"],"related_works":["https://openalex.org/W258841667","https://openalex.org/W239288174","https://openalex.org/W152009479","https://openalex.org/W2773853493","https://openalex.org/W2171849053","https://openalex.org/W2359485282","https://openalex.org/W2047706042","https://openalex.org/W2076805181","https://openalex.org/W1956208363","https://openalex.org/W1979080513"],"abstract_inverted_index":{"In":[0,62],"this":[1],"paper,":[2],"the":[3,7,17,36,55,90],"Cauchy":[4,18,87],"problem":[5,88],"for":[6,22,27,89,109],"modified":[8,91,111,142],"Helmholtz":[9,92,112],"equation":[10],"is":[11,20,33],"investigated":[12],"in":[13,35],"a":[14,41,86,110,133],"rectangle,":[15],"where":[16],"data":[19,26],"given":[21],"y=0":[23],"and":[24,29,70,81,101,105,141],"boundary":[25],"x=0":[28],"x=\u03c0.":[30],"The":[31],"solution":[32],"sought":[34],"interval":[37],"0<y\u22641.":[38],"We":[39],"propose":[40],"quasi-boundary":[42,129],"value":[43,130],"regularization":[44,143],"method":[45,76,131,138,144],"to":[46,54,84],"formulate":[47],"regularized":[48],"solutions":[49],"which":[50],"are":[51],"stably":[52],"convergent":[53],"exact":[56],"one":[57],"with":[58,77],"explicit":[59],"error":[60,107],"estimates.":[61],"addition,":[63],"we":[64],"also":[65],"carry":[66],"out":[67],"numerical":[68,72],"experiments":[69],"compare":[71],"results":[73,135],"of":[74,139,145],"our":[75,128],"Qin's":[78],"methods":[79,83,103],"[Quasi-reversibility":[80],"truncation":[82],"solve":[85],"equation,":[93,113],"Math.":[94],"Comput.":[95],"Simulation":[96],"80":[97],"(2009),":[98],"pp.":[99,123],"352\u2013366]":[100],"Tuan's":[102],"[Regularization":[104],"new":[106],"estimates":[108],"An.":[114],"Stiint":[115],"Univ.":[116],"\u2018Ovidius'":[117],"Constanta":[118],"Ser.":[119],"Mat.":[120],"18(2)":[121],"(2010),":[122],"267\u2013280].":[124],"It":[125],"shows":[126],"that":[127],"give":[132],"better":[134],"than":[136],"quasi-reversibility":[137],"Qin":[140],"Tuan.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
