{"id":"https://openalex.org/W2086430326","doi":"https://doi.org/10.1137/s1064827596306963","title":"Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods","display_name":"Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2086430326","doi":"https://doi.org/10.1137/s1064827596306963","mag":"2086430326"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596306963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596306963","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/A5102923361","display_name":"Hans Olsson","orcid":"https://orcid.org/0000-0002-8510-3484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hans Olsson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085498434","display_name":"Gustaf S\u00f6derlind","orcid":"https://orcid.org/0000-0003-3559-960X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gustaf S\u00f6derlind","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8636,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86631486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"20","issue":"1","first_page":"185","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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":0.9976999759674072,"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":0.9961000084877014,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8295083045959473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.631916880607605},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6015987992286682},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5228698253631592},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.48493340611457825},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4763891100883484},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.47075846791267395},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.46120280027389526},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4398638904094696},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.4369544982910156},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.429132878780365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.324901282787323},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3221614360809326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28803038597106934},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18778926134109497},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1688501536846161},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1086682379245758}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8295083045959473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.631916880607605},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6015987992286682},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5228698253631592},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.48493340611457825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4763891100883484},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.47075846791267395},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.46120280027389526},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4398638904094696},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.4369544982910156},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.429132878780365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.324901282787323},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3221614360809326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28803038597106934},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18778926134109497},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1688501536846161},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1086682379245758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/s1064827596306963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596306963","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W44384215","https://openalex.org/W1592421646","https://openalex.org/W1972050171","https://openalex.org/W1981084826","https://openalex.org/W1995504856","https://openalex.org/W2021412599","https://openalex.org/W2040308813","https://openalex.org/W2063507023","https://openalex.org/W2070495144","https://openalex.org/W2071006055","https://openalex.org/W2080816093","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W1979256100","https://openalex.org/W2221851535","https://openalex.org/W2154987733","https://openalex.org/W3086265770","https://openalex.org/W2742467053","https://openalex.org/W2183233158","https://openalex.org/W47811045","https://openalex.org/W3096719680","https://openalex.org/W93433166","https://openalex.org/W2071562924"],"abstract_inverted_index":{"The":[0,28],"prediction":[1,100],"of":[2,21,30,58,112,124],"stage":[3,37,60],"values":[4],"in":[5,48,92],"implicit":[6,41],"Runge--Kutta":[7],"methods":[8,42,57],"is":[9,33,63],"important":[10],"both":[11],"for":[12,18,25,40,54,75],"overall":[13],"efficiency":[14,91],"as":[15,17],"well":[16],"the":[19,26,76,81,93,99],"design":[20],"suitable":[22],"control":[23,106],"strategies":[24,107],"method.":[27],"purpose":[29],"this":[31],"paper":[32],"to":[34,44,65,88,97,104,110,116],"construct":[35],"good":[36],"value":[38],"predictors":[39],"and":[43],"verify":[45],"their":[46],"behavior":[47],"practical":[49],"computations.":[50],"We":[51,84],"show":[52],"that":[53,114],"stiffly":[55],"accurate":[56],"low":[59],"order":[61],"it":[62],"necessary":[64],"use":[66],"several":[67],"predictors.":[68],"In":[69],"other":[70],"words,":[71],"a":[72],"continuous":[73],"extension":[74],"method":[77],"will":[78],"not":[79],"yield":[80],"best":[82],"results.":[83],"also":[85],"investigate":[86],"how":[87],"gain":[89],"additional":[90],"Newton":[94],"iterations":[95],"used":[96],"correct":[98],"error.":[101],"This":[102],"leads":[103],"new":[105],"with":[108],"respect":[109],"refactorization":[111],"Jacobians":[113],"seek":[115],"globally":[117],"minimize":[118],"total":[119],"work":[120],"per":[121],"unit":[122],"time":[123],"integration.":[125]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}