{"id":"https://openalex.org/W7077048532","doi":"https://doi.org/10.48550/arxiv.2507.20266","title":"Spectral element methods for boundary-value problems of functional differential equations","display_name":"Spectral element methods for boundary-value problems of functional differential equations","publication_year":2025,"publication_date":"2025-07-27","ids":{"openalex":"https://openalex.org/W7077048532","doi":"https://doi.org/10.48550/arxiv.2507.20266"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2507.20266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.20266","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2507.20266","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"and\u00f2, Alessia","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"and\u00f2, Alessia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Sieber, Jan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sieber, Jan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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":true,"primary_topic":{"id":"https://openalex.org/T10978","display_name":"Prenatal Screening and Diagnostics","score":0.3068999946117401,"subfield":{"id":"https://openalex.org/subfields/2735","display_name":"Pediatrics, Perinatology and Child Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10978","display_name":"Prenatal Screening and Diagnostics","score":0.3068999946117401,"subfield":{"id":"https://openalex.org/subfields/2735","display_name":"Pediatrics, Perinatology and Child Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10290","display_name":"Pregnancy and preeclampsia studies","score":0.09449999779462814,"subfield":{"id":"https://openalex.org/subfields/2729","display_name":"Obstetrics and Gynecology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12552","display_name":"Fetal and Pediatric Neurological Disorders","score":0.051600001752376556,"subfield":{"id":"https://openalex.org/subfields/2735","display_name":"Pediatrics, Perinatology and Child Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.7677000164985657},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7131999731063843},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6532999873161316},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.6179999709129333},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.608299970626831},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6057000160217285},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5099999904632568},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45879998803138733},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43869999051094055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8180999755859375},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.7677000164985657},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7131999731063843},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6532999873161316},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.6179999709129333},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.608299970626831},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6057000160217285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6054999828338623},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5099999904632568},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45579999685287476},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.31790000200271606},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C4349628","wikidata":"https://www.wikidata.org/wiki/Q17027720","display_name":"hp-FEM","level":5,"score":0.2937999963760376},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2507.20266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.20266","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2507.20266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.20266","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"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":{"We":[0],"prove":[1,25],"convergence":[2,95,125],"of":[3,37,47,69,96,104],"the":[4,27,32,48,61,82,93,97,102,105,124],"spectral":[5,83],"element":[6,84],"method":[7,85],"for":[8,18,40,50,117],"piecewise":[9],"polynomial":[10],"collocation":[11,29,98],"applied":[12],"to":[13],"periodic":[14],"boundary":[15],"value":[16],"problems":[17],"functional":[19],"differential":[20,58],"equations.":[21],"In":[22],"particular,":[23],"we":[24],"that":[26,53],"numerical":[28],"solution":[30,34,99],"approximates":[31],"true":[33,106],"with":[35,72],"accuracy":[36],"order":[38],"$\\mathrm{e}^{-\u03b7m}$":[39],"some":[41],"$\u03b7>0$":[42],"and":[43,75],"increasing":[44],"degree":[45],"$m$":[46],"polynomials":[49],"a":[51,66],"case":[52],"is":[54,127],"common":[55],"in":[56,110,121],"applications:":[57],"equations":[59],"where":[60],"right-hand":[62],"side":[63],"depends":[64,100],"on":[65,101],"finite":[67,132],"number":[68],"delayed":[70],"arguments":[71],"parametric":[73],"delays":[74,81],"real":[76,114],"analytic":[77,115,118],"coefficients.":[78,119],"For":[79],"state-dependent":[80],"also":[86],"converges":[87],"under":[88],"mild":[89],"regularity":[90],"assumptions,":[91],"but":[92],"geometric":[94],"properties":[103],"solution,":[107],"which":[108],"may":[109],"general":[111],"not":[112],"be":[113],"even":[116],"However,":[120],"those":[122],"cases":[123],"rate":[126],"still":[128],"higher":[129],"than":[130],"all":[131],"orders.":[133]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}