{"id":"https://openalex.org/W3169414497","doi":"https://doi.org/10.1137/19m1258153","title":"A Variable Stepsize, Variable Order Family of Low Complexity","display_name":"A Variable Stepsize, Variable Order Family of Low Complexity","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3169414497","doi":"https://doi.org/10.1137/19m1258153","mag":"3169414497"},"language":"en","primary_location":{"id":"doi:10.1137/19m1258153","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258153","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/A5025481765","display_name":"Victor DeCaria","orcid":"https://orcid.org/0000-0002-2045-7337"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Victor DeCaria","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062068681","display_name":"Ahmet Guzel","orcid":"https://orcid.org/0000-0002-6514-9805"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ahmet Guzel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064202954","display_name":"William Layton","orcid":"https://orcid.org/0000-0002-2539-4478"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William Layton","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100421736","display_name":"Yi Li","orcid":"https://orcid.org/0000-0003-1720-2760"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025481765"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6085,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.95071068,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"43","issue":"3","first_page":"A2130","last_page":"A2160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9962999820709229,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.7791929244995117},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7051541209220886},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5326124429702759},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5281748175621033},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4619688391685486},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44789087772369385},{"id":"https://openalex.org/keywords/adaptive-stepsize","display_name":"Adaptive stepsize","score":0.43621906638145447},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4253336489200592},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.41796499490737915},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39545220136642456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36925333738327026},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.35584068298339844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25221478939056396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10338026285171509}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7791929244995117},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7051541209220886},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5326124429702759},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5281748175621033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4619688391685486},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44789087772369385},{"id":"https://openalex.org/C48077252","wikidata":"https://www.wikidata.org/wiki/Q4680766","display_name":"Adaptive stepsize","level":3,"score":0.43621906638145447},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4253336489200592},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.41796499490737915},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39545220136642456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36925333738327026},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.35584068298339844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25221478939056396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10338026285171509},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1258153","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258153","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/G3253501796","display_name":null,"funder_award_id":"CBET-1609120","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5323941380","display_name":null,"funder_award_id":"201706280334","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G5424558681","display_name":null,"funder_award_id":"DMS-1817542","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6519594075","display_name":null,"funder_award_id":"DMS-1522267","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6884055810","display_name":null,"funder_award_id":"11571274","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/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1691509152","https://openalex.org/W1983932402","https://openalex.org/W1984969067","https://openalex.org/W1993309344","https://openalex.org/W2001393739","https://openalex.org/W2004759358","https://openalex.org/W2010165577","https://openalex.org/W2014574992","https://openalex.org/W2017044842","https://openalex.org/W2019291954","https://openalex.org/W2026646621","https://openalex.org/W2027822086","https://openalex.org/W2035324740","https://openalex.org/W2041851395","https://openalex.org/W2069967992","https://openalex.org/W2073851030","https://openalex.org/W2076077791","https://openalex.org/W2077552255","https://openalex.org/W2077657920","https://openalex.org/W2095392846","https://openalex.org/W2098195885","https://openalex.org/W2117239908","https://openalex.org/W2128612765","https://openalex.org/W2134781512","https://openalex.org/W2139376510","https://openalex.org/W2163998724","https://openalex.org/W2164622471","https://openalex.org/W2171297539","https://openalex.org/W2325083198","https://openalex.org/W2325830745","https://openalex.org/W2345742189","https://openalex.org/W2409648791","https://openalex.org/W2410416051","https://openalex.org/W2477880479","https://openalex.org/W2634579303","https://openalex.org/W2742266772","https://openalex.org/W2791068112","https://openalex.org/W2963632047","https://openalex.org/W2964183919","https://openalex.org/W4235712333"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W1976205134","https://openalex.org/W2381570729","https://openalex.org/W2258597548","https://openalex.org/W2894810616","https://openalex.org/W2226986557","https://openalex.org/W2897864634","https://openalex.org/W2621722902","https://openalex.org/W3169414497"],"abstract_inverted_index":{"Variable":[0],"stepsize,":[1],"variable":[2,88],"order":[3,96],"(VSVO)":[4],"methods":[5,11,38,75],"have":[6],"limited":[7],"impact":[8],"in":[9,12,23,26],"timestepping":[10],"complex":[13],"applications":[14],"due":[15],"to":[16,60],"their":[17],"computational":[18,85],"complexity":[19,86],"and":[20,71,80,102],"the":[21,54,83,95,98],"difficulty":[22],"implementing":[24],"them":[25],"an":[27],"existing":[28],"code.":[29],"We":[30],"introduce":[31],"a":[32],"family":[33],"of":[34,53,63,76,93,97],"implicit,":[35],"embedded":[36],"VSVO":[37,74],"that":[39],"require":[40,105],"only":[41],"one":[42],"BDF":[43],"solve":[44],"at":[45,56],"each":[46],"timestep":[47],"followed":[48],"by":[49],"adding":[50],"linear":[51],"combinations":[52],"solution":[55],"previous":[57],"time":[58],"levels":[59],"compute":[61],"solutions":[62],"different":[64],"order.":[65],"In":[66],"particular,":[67],"we":[68],"construct":[69],"implicit":[70,73],"linearly":[72],"orders":[77],"two,":[78],"three,":[79],"four":[81],"with":[82],"same":[84],"as":[87],"stepsize":[89],"BDF3.":[90],"The":[91],"choice":[92],"changing":[94],"method":[99],"is":[100],"simple":[101],"does":[103],"not":[104],"additional":[106],"nonlinear":[107],"system":[108],"solves.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}