{"id":"https://openalex.org/W2755570977","doi":"https://doi.org/10.1137/16m1090107","title":"Numerical Solution of the Nonlocal Diffusion Equation on the Real Line","display_name":"Numerical Solution of the Nonlocal Diffusion Equation on the Real Line","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2755570977","doi":"https://doi.org/10.1137/16m1090107","mag":"2755570977"},"language":"en","primary_location":{"id":"doi:10.1137/16m1090107","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1090107","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5102804383","display_name":"Chunxiong Zheng","orcid":"https://orcid.org/0000-0001-5735-633X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chunxiong Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018259595","display_name":"Jiashun Hu","orcid":"https://orcid.org/0000-0003-0020-3492"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiashun Hu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100353054","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0003-3273-5581"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiwei Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8645,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.83720384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"39","issue":"5","first_page":"A1951","last_page":"A1968"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.7956517338752747},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.741814136505127},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.720850944519043},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5674483776092529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5442928671836853},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5207062363624573},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5150734782218933},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4825419783592224},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4727436304092407},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.4317690134048462},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4209012985229492},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.42053359746932983},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4203314185142517},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4027549624443054},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1907981038093567}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7956517338752747},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.741814136505127},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.720850944519043},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5674483776092529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5442928671836853},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5207062363624573},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5150734782218933},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4825419783592224},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4727436304092407},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.4317690134048462},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4209012985229492},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.42053359746932983},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4203314185142517},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4027549624443054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1907981038093567},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1090107","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1090107","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2746842099","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3129806459","display_name":null,"funder_award_id":"11371218","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4143625290","display_name":null,"funder_award_id":"DMS-1315259","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4191609294","display_name":null,"funder_award_id":"W911NF-15-1-0562","funder_id":"https://openalex.org/F4320332201","funder_display_name":"Office of the Secretary of Defense"},{"id":"https://openalex.org/G5405721928","display_name":null,"funder_award_id":"U1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7633975376","display_name":null,"funder_award_id":"DMS-1318586","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G890820059","display_name":null,"funder_award_id":"11771035","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"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/F4320332201","display_name":"Office of the Secretary of Defense","ror":"https://ror.org/00q4sx826"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W193865898","https://openalex.org/W1128483265","https://openalex.org/W1591798773","https://openalex.org/W1973127220","https://openalex.org/W1978147630","https://openalex.org/W1995631063","https://openalex.org/W2001730319","https://openalex.org/W2003530198","https://openalex.org/W2006044588","https://openalex.org/W2009787868","https://openalex.org/W2011095781","https://openalex.org/W2011572440","https://openalex.org/W2012828992","https://openalex.org/W2015699640","https://openalex.org/W2015983313","https://openalex.org/W2016823491","https://openalex.org/W2026508990","https://openalex.org/W2029529153","https://openalex.org/W2036662074","https://openalex.org/W2045670796","https://openalex.org/W2053012267","https://openalex.org/W2058999263","https://openalex.org/W2067352798","https://openalex.org/W2068110329","https://openalex.org/W2068823890","https://openalex.org/W2069492372","https://openalex.org/W2079454536","https://openalex.org/W2092046487","https://openalex.org/W2093971242","https://openalex.org/W2111271983","https://openalex.org/W2125526756","https://openalex.org/W2137766864","https://openalex.org/W2139045013","https://openalex.org/W2163377433","https://openalex.org/W2463117017","https://openalex.org/W2550897446","https://openalex.org/W2560332956"],"related_works":["https://openalex.org/W1963845699","https://openalex.org/W2035232447","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2144321310","https://openalex.org/W2001419904","https://openalex.org/W1994364604","https://openalex.org/W2060217354","https://openalex.org/W1982234448","https://openalex.org/W2061461757"],"abstract_inverted_index":{"Numerical":[0,113],"computation":[1],"of":[2,41,50,121],"a":[3,26,60,64],"nonlocal":[4,28],"diffusion":[5,29],"equation":[6],"on":[7,31,46,63],"the":[8,42,47,51,78,92,99,105,110,119],"real":[9],"axis":[10],"is":[11],"considered":[12],"in":[13],"this":[14],"paper.":[15],"We":[16],"first":[17],"apply":[18,98],"an":[19,32,38,68,84],"extensively":[20],"studied":[21],"quadrature":[22,101],"scheme":[23],"to":[24,76,103,117],"obtain":[25],"discrete":[27,43],"system":[30,61],"unbounded":[33],"domain.":[34],"Then":[35],"we":[36,97],"derive":[37],"alternative":[39],"formulation":[40,55],"problem":[44,82],"based":[45],"spectral":[48],"analysis":[49],"$z$-transform.":[52,112],"This":[53],"new":[54],"can":[56],"be":[57],"seen":[58],"as":[59],"defined":[62],"bounded":[65,86],"domain":[66,81,87],"with":[67],"artificial":[69,94],"boundary":[70,95],"condition,":[71,96],"and":[72],"it":[73],"allows":[74],"us":[75],"reformulate":[77],"original":[79],"infinite":[80],"into":[83],"equivalent":[85],"problem.":[88],"To":[89],"numerically":[90],"implement":[91],"exact":[93],"trapezoidal":[100],"rule":[102],"approximate":[104],"contour":[106],"integral":[107],"induced":[108],"by":[109],"inverse":[111],"examples":[114],"are":[115],"presented":[116],"demonstrate":[118],"effectiveness":[120],"our":[122],"approach.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}