{"id":"https://openalex.org/W7163322198","doi":"https://doi.org/10.48550/arxiv.2606.03516","title":"Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations","display_name":"Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163322198","doi":"https://doi.org/10.48550/arxiv.2606.03516"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03516","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.03516","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137744779","display_name":"Guanglian Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Guanglian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113057247","display_name":"Qingle Lin","orcid":"https://orcid.org/0009-0006-2493-7043"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Qingle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137772360","display_name":"Shu-lin Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Shu-lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137737250","display_name":"Zhi Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Zhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9805999994277954,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9805999994277954,"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":0.002300000051036477,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/convergence","display_name":"Convergence (economics)","score":0.7785999774932861},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6366000175476074},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.5924000144004822},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5777999758720398},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.42260000109672546},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4113999903202057},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.40720000863075256},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.38609999418258667}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7785999774932861},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7542999982833862},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6366000175476074},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.5924000144004822},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5777999758720398},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5436000227928162},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.42260000109672546},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.40720000863075256},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.3734999895095825},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.3695000112056732},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.3564000129699707},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.3490999937057495},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2838999927043915},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27889999747276306},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26249998807907104},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.26179999113082886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03516","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.03516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03516","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Long-time":[0],"simulations":[1],"of":[2,15,78,107,131,157,171],"evolution":[3],"equations":[4,86],"present":[5],"substantial":[6],"computational":[7],"challenges":[8],"due":[9],"to":[10,31,54,154],"the":[11,33,39,52,59,75,79,104,108,117,123,127,132,155,158,164,168,182],"inherently":[12],"sequential":[13],"nature":[14],"conventional":[16],"time-stepping":[17],"schemes.":[18],"The":[19,120,161],"parareal":[20,80,109,133],"method,":[21,134],"a":[22,28,67,113,135],"leading":[23],"parallel-in-time":[24],"(PinT)":[25],"algorithm,":[26],"offers":[27],"promising":[29],"approach":[30],"overcome":[32],"challenge":[34],"by":[35],"introducing":[36],"concurrency":[37],"in":[38],"time":[40],"domain.":[41],"While":[42],"its":[43],"convergence":[44,76,106,118,129,138,169],"theory":[45,53,139],"is":[46],"well-established":[47],"for":[48,82,116,140],"linear":[49,105,137,141,176],"problems,":[50,56],"extending":[51],"nonlinear":[55,172],"particularly":[57],"when":[58],"problem":[60,159],"data":[61],"have":[62],"only":[63],"limited":[64],"regularity,":[65],"remains":[66],"significant":[68],"challenge.":[69],"In":[70],"this":[71],"work,":[72],"we":[73],"provide":[74,112],"analysis":[77,121,130,162],"algorithm":[81,110],"solving":[83],"semilinear":[84],"parabolic":[85,142],"with":[87,152],"an":[88],"$H^2$":[89],"initial":[90],"data.":[91,160],"We":[92],"employ":[93],"stable":[94],"rational":[95],"approximations":[96],"and":[97,111,144,174],"first-order":[98],"linearization":[99],"as":[100],"coarse":[101],"propagators,":[102],"establish":[103],"sharp":[114],"estimate":[115],"factor.":[119],"combines":[122],"error-splitting":[124],"technique":[125],"from":[126],"superlinear":[128],"refined":[136],"equations,":[143],"\\textsl{a":[145],"priori}":[146],"error":[147],"estimates":[148],"that":[149],"are":[150],"optimal":[151],"respect":[153],"regularity":[156],"shows":[163],"close":[165],"connection":[166],"between":[167],"behavior":[170],"models":[173],"their":[175],"counterparts.":[177],"Numerical":[178],"experiments":[179],"fully":[180],"support":[181],"theoretical":[183],"findings.":[184]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-04T00:00:00"}