{"id":"https://openalex.org/W2012590081","doi":"https://doi.org/10.1080/00207160.2015.1012837","title":"Rosenbrock methods with an explicit first stage","display_name":"Rosenbrock methods with an explicit first stage","publication_year":2015,"publication_date":"2015-02-18","ids":{"openalex":"https://openalex.org/W2012590081","doi":"https://doi.org/10.1080/00207160.2015.1012837","mag":"2012590081"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1012837","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1012837","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5008436217","display_name":"Adrian Sandu","orcid":"https://orcid.org/0000-0002-5380-0103"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Adrian Sandu","raw_affiliation_strings":["Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA","Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA24060, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA24060, USA#TAB#","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008436217"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07378877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":"6","first_page":"995","last_page":"1010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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":0.7051162123680115},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6560903787612915},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6305869817733765},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5623642802238464},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5312219858169556},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49419882893562317},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4890314042568207},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4450850188732147},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.43874385952949524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3590642809867859},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29123830795288086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17817282676696777},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05708923935890198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7051162123680115},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6560903787612915},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6305869817733765},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5623642802238464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5312219858169556},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49419882893562317},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4890314042568207},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4450850188732147},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.43874385952949524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3590642809867859},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29123830795288086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17817282676696777},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05708923935890198},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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:10.1080/00207160.2015.1012837","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1012837","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G497177525","display_name":null,"funder_award_id":"CCF-0916493,CCF-1218454,CMMI-1130667,DMS-0915047,OCI-8670904397","funder_id":"https://openalex.org/F4320332179","funder_display_name":"Office of the Director"},{"id":"https://openalex.org/G8123802660","display_name":null,"funder_award_id":"12-2640-06,FA9550-12-1-0293-DEF","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320332179","display_name":"Office of the Director","ror":"https://ror.org/04nseet23"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1902819800","https://openalex.org/W1999756879","https://openalex.org/W2055070885","https://openalex.org/W2059330316","https://openalex.org/W2067870952","https://openalex.org/W2079038427","https://openalex.org/W2095219532"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W1976205134","https://openalex.org/W2381570729","https://openalex.org/W4248336175","https://openalex.org/W3009369890","https://openalex.org/W2031260042","https://openalex.org/W2391445434","https://openalex.org/W4312490297","https://openalex.org/W2196719869"],"abstract_inverted_index":{"Traditional":[0],"Rosenbrock":[1,26],"methods":[2],"suffer":[3,48],"from":[4,49],"order":[5,50,56],"reduction":[6],"when":[7],"applied":[8],"to":[9,37,79],"partial":[10,83],"differential":[11,84],"equations":[12,85],"with":[13,28,40],"non-homogeneous":[14],"boundary":[15],"conditions":[16,57],"and":[17,44,66,70,76,81],"source":[18],"terms.":[19],"The":[20,52],"paper":[21,53],"studies":[22],"a":[23],"family":[24],"of":[25],"schemes":[27,73],"an":[29],"explicit":[30],"first":[31],"stage.":[32],"This":[33],"structure":[34],"allows":[35],"one":[36],"construct":[38],"algorithms":[39],"high":[41],"stage":[42],"orders,":[43],"which":[45],"do":[46],"not":[47],"reduction.":[51],"discusses":[54],"additional":[55],"needed":[58],"for":[59,62],"linear":[60],"stability,":[61],"using":[63],"inexact":[64],"Jacobians,":[65],"implementation":[67],"aspects.":[68],"Second-":[69],"third-order":[71],"practical":[72],"are":[74],"constructed,":[75],"their":[77],"application":[78],"one-":[80],"two-dimensional":[82],"test":[86],"problems":[87],"confirm":[88],"the":[89],"theoretical":[90],"findings.":[91]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
