{"id":"https://openalex.org/W4319068674","doi":"https://doi.org/10.1137/22m1492842","title":"A Generic and Strictly Banded Spectral Petrov\u2013Galerkin Method for Differential Equations with Polynomial Coefficients","display_name":"A Generic and Strictly Banded Spectral Petrov\u2013Galerkin Method for Differential Equations with Polynomial Coefficients","publication_year":2023,"publication_date":"2023-02-03","ids":{"openalex":"https://openalex.org/W4319068674","doi":"https://doi.org/10.1137/22m1492842"},"language":"en","primary_location":{"id":"doi:10.1137/22m1492842","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1492842","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10852/99687","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033984993","display_name":"Mikael Mortensen","orcid":"https://orcid.org/0000-0002-3293-7573"},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Mikael Mortensen","raw_affiliation_strings":["Department of Mathematics, Division of Mechanics, University of Oslo, Oslo 0851, Norway"],"raw_orcid":"https://orcid.org/0000-0002-3293-7573","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Division of Mechanics, University of Oslo, Oslo 0851, Norway","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033984993"],"corresponding_institution_ids":["https://openalex.org/I184942183"],"apc_list":null,"apc_paid":null,"fwci":1.5931,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77730461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"45","issue":"1","first_page":"A123","last_page":"A146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8870696425437927},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.7404763102531433},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6263458132743835},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6045323014259338},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.6020787358283997},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5429929494857788},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.4955047369003296},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.4892387390136719},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.48089101910591125},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46596458554267883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46408864855766296},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.46295055747032166},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.45755019783973694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4566776156425476},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.43534865975379944},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43451589345932007},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.42103564739227295},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.41068288683891296},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3021441102027893},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21099534630775452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8870696425437927},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.7404763102531433},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6263458132743835},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6045323014259338},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.6020787358283997},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5429929494857788},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.4955047369003296},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.4892387390136719},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.48089101910591125},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46596458554267883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46408864855766296},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.46295055747032166},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.45755019783973694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4566776156425476},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.43534865975379944},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43451589345932007},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.42103564739227295},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.41068288683891296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3021441102027893},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21099534630775452},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1492842","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1492842","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"},{"id":"pmh:oai:www.duo.uio.no:10852/99687","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/99687","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1064-8275","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.duo.uio.no:10852/99687","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/99687","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1064-8275","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1523273974","https://openalex.org/W1635622277","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1985144286","https://openalex.org/W2002391771","https://openalex.org/W2023271554","https://openalex.org/W2023988191","https://openalex.org/W2039707205","https://openalex.org/W2041381172","https://openalex.org/W2048028343","https://openalex.org/W2052539747","https://openalex.org/W2055738068","https://openalex.org/W2056658486","https://openalex.org/W2082849992","https://openalex.org/W2090043357","https://openalex.org/W2097091963","https://openalex.org/W2108473871","https://openalex.org/W2130655033","https://openalex.org/W2158575547","https://openalex.org/W2166245316","https://openalex.org/W2171692351","https://openalex.org/W2273606872","https://openalex.org/W2410898212","https://openalex.org/W2807920410","https://openalex.org/W2901197498","https://openalex.org/W2944878488","https://openalex.org/W2963672055","https://openalex.org/W3101826276","https://openalex.org/W3123764437","https://openalex.org/W3196429337","https://openalex.org/W4253937035","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2793709684","https://openalex.org/W2493096353","https://openalex.org/W1896660781","https://openalex.org/W4298399453","https://openalex.org/W2005041925","https://openalex.org/W225326886","https://openalex.org/W1835390889","https://openalex.org/W2045154321","https://openalex.org/W2937107277","https://openalex.org/W3172249873"],"abstract_inverted_index":{"In":[0],"this":[1,75],"paper":[2],"we":[3],"describe":[4],"a":[5,87,104],"generic":[6],"spectral":[7],"Petrov\u2013Galerkin":[8,97],"method":[9,26,76,98,123],"that":[10,85],"is":[11,101],"sparse":[12],"and":[13,36,45,65,99,126],"strictly":[14,114],"banded":[15,115],"for":[16,108],"any":[17],"linear":[18],"ordinary":[19],"differential":[20],"equation":[21],"with":[22],"polynomial":[23],"coefficients.":[24],"The":[25],"applies":[27],"to":[28,47,79,128],"all":[29,118],"subdivisions":[30],"of":[31,42,54,82,112,117,134],"Jacobi":[32,109],"polynomials":[33],"(e.g.,":[34],"Chebyshev":[35],"Legendre),":[37],"utilizes":[38],"well-known":[39],"recurrence":[40],"relations":[41],"orthogonal":[43],"polynomials,":[44],"leads":[46],"almost":[48],"exactly":[49],"the":[50,57,95,113,121,132],"same":[51],"discretized":[52],"system":[53],"equations":[55],"as":[56],"integration":[58],"preconditioners":[59],"[E.":[60],"A.":[61],"Coutsias,":[62],"T.":[63],"Hagstrom,":[64],"D.":[66],"Torres,":[67],"Math.":[68],"Comp.,":[69],"65":[70],"(1996),":[71],"pp.":[72],"611\u2013635]":[73],"if":[74],"was":[77],"redesigned":[78],"make":[80],"use":[81,133],"trial":[83],"functions":[84],"satisfy":[86],"given":[88],"problem\u2019s":[89],"boundary":[90],"conditions.":[91],"A":[92],"link":[93],"between":[94],"new":[96,105,122],"IP":[100],"revealed":[102],"through":[103],"recursion":[106],"relation":[107],"polynomials.":[110],"Because":[111],"nature":[116],"coefficient":[119],"matrices,":[120],"extends":[124],"easily":[125],"efficiently":[127],"multiple":[129],"dimensions":[130],"though":[131],"tensor":[135],"product":[136],"methods.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}
