{"id":"https://openalex.org/W2158439065","doi":"https://doi.org/10.1080/00207169708804616","title":"Continuous extensions to high order runge-kutta methods","display_name":"Continuous extensions to high order runge-kutta methods","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2158439065","doi":"https://doi.org/10.1080/00207169708804616","mag":"2158439065"},"language":"en","primary_location":{"id":"doi:10.1080/00207169708804616","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804616","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":true,"oa_status":"green","oa_url":"http://doi.org/10.1080/00207169708804616","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051235431","display_name":"George Papageorgiou","orcid":"https://orcid.org/0000-0002-3725-4499"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"G. Papageorgiou","raw_affiliation_strings":["Department of Mathematics , National Technical University of Athens , Zografou Campus, Athens, 15780"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , National Technical University of Athens , Zografou Campus, Athens, 15780","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006207605","display_name":"Ch. Tsitouras","orcid":"https://orcid.org/0000-0001-6801-8117"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Ch. Tsitouras","raw_affiliation_strings":["Department of Mathematics , National Technical University of Athens , Zografou Campus, Athens, 15780"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , National Technical University of Athens , Zografou Campus, Athens, 15780","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051235431"],"corresponding_institution_ids":["https://openalex.org/I174458059"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.28801743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"65","issue":"3-4","first_page":"273","last_page":"291"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9970999956130981,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.9194663763046265},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7174124717712402},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6415210962295532},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5496644377708435},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5313314199447632},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5134073495864868},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5093103647232056},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.49709179997444153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3600791096687317},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3338291049003601},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3143962025642395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2431507110595703},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2392929494380951},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.07998937368392944}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9194663763046265},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7174124717712402},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6415210962295532},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5496644377708435},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5313314199447632},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5134073495864868},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5093103647232056},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.49709179997444153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3600791096687317},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3338291049003601},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3143962025642395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2431507110595703},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2392929494380951},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.07998937368392944},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207169708804616","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804616","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"},{"id":"pmh:oai:dspace.lib.ntua.gr:123456789/12212","is_oa":true,"landing_page_url":"http://doi.org/10.1080/00207169708804616","pdf_url":null,"source":{"id":"https://openalex.org/S4377196837","display_name":"DSpace - NTUA (National Technical University of Athens)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I174458059","host_organization_name":"National Technical University of Athens","host_organization_lineage":["https://openalex.org/I174458059"],"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":"International Journal of Computer Mathematics","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dspace.lib.ntua.gr:123456789/12212","is_oa":true,"landing_page_url":"http://doi.org/10.1080/00207169708804616","pdf_url":null,"source":{"id":"https://openalex.org/S4377196837","display_name":"DSpace - NTUA (National Technical University of Athens)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I174458059","host_organization_name":"National Technical University of Athens","host_organization_lineage":["https://openalex.org/I174458059"],"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":"International Journal of Computer Mathematics","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":21,"referenced_works":["https://openalex.org/W114660188","https://openalex.org/W1964214402","https://openalex.org/W1969122636","https://openalex.org/W1973230957","https://openalex.org/W1977525595","https://openalex.org/W1985494751","https://openalex.org/W1987456624","https://openalex.org/W1998868738","https://openalex.org/W2000397373","https://openalex.org/W2007255973","https://openalex.org/W2008542229","https://openalex.org/W2015736664","https://openalex.org/W2021910005","https://openalex.org/W2029416092","https://openalex.org/W2042514790","https://openalex.org/W2061376823","https://openalex.org/W2074178332","https://openalex.org/W2085471512","https://openalex.org/W2144144709","https://openalex.org/W2169062786","https://openalex.org/W4210871879"],"related_works":["https://openalex.org/W1611524765","https://openalex.org/W2358067891","https://openalex.org/W4384827542","https://openalex.org/W2362691724","https://openalex.org/W2076442606","https://openalex.org/W2105326322","https://openalex.org/W1629396682","https://openalex.org/W2562925856","https://openalex.org/W2799944245","https://openalex.org/W60612525"],"abstract_inverted_index":{"Computer":[0],"assisted":[1],"derivation":[2],"and":[3,76,99],"improved":[4],"techniques":[5],"have":[6],"led":[7],"to":[8,28,39],"effective":[9],"explicit":[10],"Runge-Kutta":[11,41,71],"methods":[12,17,42,72],"of":[13,57,73,93],"higher":[14],"order.":[15],"These":[16,80],"become":[18],"inefficient":[19],"when":[20],"the":[21],"step":[22,109],"size":[23],"must":[24],"be":[25,51],"reduced":[26],"often":[27],"produce":[29],"approximations":[30,49],"at":[31,54],"specified":[32],"points.":[33],"Considerable":[34],"effort":[35],"has":[36],"been":[37],"devoted":[38],"providing":[40],"with":[43],"an":[44],"interpolation":[45],"capability,":[46],"so":[47],"that":[48],"can":[50],"produced":[52],"inexpensively":[53],"intermediate":[55],"points":[56],"a":[58],"successful":[59],"step.":[60],"New":[61],"high":[62],"order":[63],"Hermite":[64],"interpolants":[65,81],"for":[66],"two":[67,87],"well":[68],"known":[69],"embedded":[70],"orders":[74],"7":[75],"8":[77],"are":[78,82,91],"presented.":[79],"constructed":[83],"using":[84],"values":[85],"from":[86],"successive":[88],"integration":[89],"steps,":[90],"locally":[92],"O(h":[94,97],"8)":[95],"or":[96,103],"9),":[98],"require":[100],"only":[101],"one":[102],"four":[104],"extra":[105],"function":[106],"evaluations":[107],"per":[108],"respectively.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}