{"id":"https://openalex.org/W1994678449","doi":"https://doi.org/10.1137/120876241","title":"Parallel in Time Algorithm with Spectral-Subdomain Enhancement for Volterra Integral Equations","display_name":"Parallel in Time Algorithm with Spectral-Subdomain Enhancement for Volterra Integral Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1994678449","doi":"https://doi.org/10.1137/120876241","mag":"1994678449"},"language":"en","primary_location":{"id":"doi:10.1137/120876241","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876241","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/A5033250527","display_name":"Xianjuan Li","orcid":"https://orcid.org/0000-0001-5456-4395"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianjuan Li","raw_affiliation_strings":["Fuzhou University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fuzhou University","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058967726","display_name":"Tao Tang","orcid":"https://orcid.org/0000-0003-2919-2774"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tao Tang","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013537195","display_name":"Chuanju Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuanju Xu","raw_affiliation_strings":["Xiamen University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xiamen University","institution_ids":["https://openalex.org/I191208505"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5983,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.94095203,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"51","issue":"3","first_page":"1735","last_page":"1756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9980000257492065,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9945999979972839,"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/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6546623110771179},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6525543332099915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6397461295127869},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6368969082832336},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6000398397445679},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5934622287750244},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5191808938980103},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.50714111328125},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4944427013397217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4825591444969177},{"id":"https://openalex.org/keywords/time-domain","display_name":"Time domain","score":0.4810919463634491},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4779122769832611},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.47305217385292053},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.435366690158844},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.43377089500427246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36174559593200684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29099228978157043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22628700733184814},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18013355135917664},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.10588374733924866},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.0869722068309784}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6546623110771179},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6525543332099915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6397461295127869},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6368969082832336},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6000398397445679},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5934622287750244},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5191808938980103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.50714111328125},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4944427013397217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4825591444969177},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.4810919463634491},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4779122769832611},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.47305217385292053},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.435366690158844},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.43377089500427246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36174559593200684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29099228978157043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22628700733184814},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18013355135917664},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.10588374733924866},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0869722068309784},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120876241","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876241","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:CiteSeerX.psu:10.1.1.745.8959","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.8959","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1305.2712.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W205381016","https://openalex.org/W640428934","https://openalex.org/W1527509447","https://openalex.org/W1567668233","https://openalex.org/W1823531150","https://openalex.org/W1978958071","https://openalex.org/W1979475531","https://openalex.org/W1999103577","https://openalex.org/W2022694169","https://openalex.org/W2027491117","https://openalex.org/W2030146312","https://openalex.org/W2031567600","https://openalex.org/W2055212013","https://openalex.org/W2065699917","https://openalex.org/W2089181747","https://openalex.org/W2105970221","https://openalex.org/W2116226692","https://openalex.org/W2151640244"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2131278000","https://openalex.org/W2889856026","https://openalex.org/W2009058751","https://openalex.org/W2478942264","https://openalex.org/W1989122168"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,49,54,59,106],"parallel":[4,22,50],"in":[5,23,48,64,72,109,116],"time":[6,9,24,79],"(also":[7],"called":[8],"parareal)":[10],"method":[11,81,100,138],"to":[12,89,123],"solve":[13],"Volterra":[14],"integral":[15,86],"equations":[16],"of":[17,29,35,39,57,95,126,135,158],"the":[18,27,30,37,46,85,93,110,136,146,154],"second":[19],"kind.":[20,97],"The":[21,98,141],"approach":[25],"follows":[26],"spirit":[28],"domain":[31,38,112],"decomposition":[32],"that":[33,145],"consists":[34],"breaking":[36],"computation":[40],"into":[41],"subdomains":[42,65,117],"and":[43],"solving":[44],"iteratively":[45],"subproblems":[47],"way.":[51],"To":[52],"obtain":[53],"high":[55,128],"order":[56],"accuracy,":[58],"spectral":[60,120,156],"collocation":[61],"accuracy":[62],"enhancement":[63],"will":[66],"be":[67,161],"employed.":[68],"Our":[69],"main":[70],"contributions":[71],"this":[73],"work":[74],"are":[75],"twofold:":[76],"(i)":[77],"A":[78,131],"parareal":[80],"is":[82,92,101,139,150],"designed":[83],"for":[84],"equations,":[87],"which":[88],"our":[90],"knowledge":[91],"first":[94],"its":[96],"new":[99],"an":[102,124],"iterative":[103],"process":[104],"combining":[105],"coarse":[107],"prediction":[108],"whole":[111],"with":[113],"fine":[114],"corrections":[115],"by":[118],"using":[119],"approximation,":[121],"leading":[122],"algorithm":[125],"very":[127],"accuracy.":[129],"(ii)":[130],"rigorous":[132],"convergence":[133,159],"analysis":[134],"overall":[137,147],"provided.":[140],"numerical":[142],"experiment":[143],"confirms":[144],"computational":[148],"cost":[149],"considerably":[151],"reduced":[152],"while":[153],"desired":[155],"rate":[157],"can":[160],"obtained.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}