{"id":"https://openalex.org/W2792624595","doi":"https://doi.org/10.1007/s11075-018-0489-z","title":"Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation","display_name":"Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation","publication_year":2018,"publication_date":"2018-02-19","ids":{"openalex":"https://openalex.org/W2792624595","doi":"https://doi.org/10.1007/s11075-018-0489-z","mag":"2792624595"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-018-0489-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-018-0489-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5064395430","display_name":"Herman D. Schaumburg","orcid":"https://orcid.org/0000-0002-9803-895X"},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Herman D. Schaumburg","raw_affiliation_strings":["Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA"],"raw_orcid":"https://orcid.org/0000-0002-9803-895X","affiliations":[{"raw_affiliation_string":"Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA","institution_ids":["https://openalex.org/I102502594"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052668354","display_name":"Afnan Al Marzouk","orcid":"https://orcid.org/0000-0002-4451-7381"},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Afnan Al Marzouk","raw_affiliation_strings":["Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA","institution_ids":["https://openalex.org/I102502594"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034238833","display_name":"B. Erd\u00e9lyi","orcid":"https://orcid.org/0000-0002-9466-4320"},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bela Erdelyi","raw_affiliation_strings":["Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Northern Illinois University, DeKalb, IL, 60115, USA","institution_ids":["https://openalex.org/I102502594"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064395430"],"corresponding_institution_ids":["https://openalex.org/I102502594"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3411,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51641239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"80","issue":"2","first_page":"377","last_page":"396"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.992900013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.9400447010993958},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7056024074554443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6322965621948242},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6066595911979675},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.5585181713104248},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.476005882024765},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.47538530826568604},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.46456944942474365},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45200955867767334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4487999379634857},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4411742687225342},{"id":"https://openalex.org/keywords/numerical-differentiation","display_name":"Numerical differentiation","score":0.4132794141769409},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.4123036861419678},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3753613829612732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2901434302330017},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.24525585770606995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1770939826965332},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.15844210982322693}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.9400447010993958},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7056024074554443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6322965621948242},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6066595911979675},{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.5585181713104248},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.476005882024765},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.47538530826568604},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.46456944942474365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45200955867767334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4487999379634857},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4411742687225342},{"id":"https://openalex.org/C154181440","wikidata":"https://www.wikidata.org/wiki/Q1683292","display_name":"Numerical differentiation","level":2,"score":0.4132794141769409},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.4123036861419678},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3753613829612732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2901434302330017},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.24525585770606995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1770939826965332},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.15844210982322693},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-018-0489-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-018-0489-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1111313548","display_name":null,"funder_award_id":"DE-SC0005823","funder_id":"https://openalex.org/F4320337512","funder_display_name":"Nuclear Physics"}],"funders":[{"id":"https://openalex.org/F4320337512","display_name":"Nuclear Physics","ror":"https://ror.org/02atag894"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W409181815","https://openalex.org/W1480066506","https://openalex.org/W1519422254","https://openalex.org/W1521738998","https://openalex.org/W1526547736","https://openalex.org/W1537372611","https://openalex.org/W1552535138","https://openalex.org/W1604849998","https://openalex.org/W1964070472","https://openalex.org/W1974537499","https://openalex.org/W1995249182","https://openalex.org/W2004170125","https://openalex.org/W2042388195","https://openalex.org/W2049142126","https://openalex.org/W2086900155","https://openalex.org/W2153455207","https://openalex.org/W2289917552","https://openalex.org/W2313721366","https://openalex.org/W2494659345","https://openalex.org/W2523257342","https://openalex.org/W2557402268","https://openalex.org/W2559569294","https://openalex.org/W3101169391","https://openalex.org/W4235516915","https://openalex.org/W4244063180","https://openalex.org/W4298282228","https://openalex.org/W6726958733"],"related_works":["https://openalex.org/W4230546540","https://openalex.org/W1543341614","https://openalex.org/W2553993726","https://openalex.org/W2593872707","https://openalex.org/W2039953621","https://openalex.org/W2026155714","https://openalex.org/W1738251596","https://openalex.org/W1966050627","https://openalex.org/W2390741385","https://openalex.org/W4254216217"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}