{"id":"https://openalex.org/W2028157765","doi":"https://doi.org/10.1090/s0025-5718-96-00718-1","title":"A family of fifth-order Runge-Kutta pairs","display_name":"A family of fifth-order Runge-Kutta pairs","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2028157765","doi":"https://doi.org/10.1090/s0025-5718-96-00718-1","mag":"2028157765"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00718-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00718-1","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00718-1/S0025-5718-96-00718-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00718-1/S0025-5718-96-00718-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015888042","display_name":"Spiros Papakostas","orcid":"https://orcid.org/0000-0002-5563-0048"},"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":"S. Papakostas","raw_affiliation_strings":["Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens 157 80, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens 157 80, Greece","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"last","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":false,"raw_author_name":"G. Papageorgiou","raw_affiliation_strings":["Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens 157 80, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens 157 80, Greece","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015888042"],"corresponding_institution_ids":["https://openalex.org/I174458059"],"apc_list":null,"apc_paid":null,"fwci":0.9637,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.74302698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"65","issue":"215","first_page":"1165","last_page":"1181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9912999868392944,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9861999750137329,"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/algorithm","display_name":"Algorithm","score":0.7169457077980042},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.6070079207420349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4985179901123047},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44169628620147705},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40023165941238403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34286564588546753},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06643372774124146}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7169457077980042},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.6070079207420349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4985179901123047},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44169628620147705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40023165941238403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34286564588546753},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06643372774124146},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-96-00718-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00718-1","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00718-1/S0025-5718-96-00718-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.107.387","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.107.387","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1996-65-215/S0025-5718-96-00718-1/S0025-5718-96-00718-1.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.lib.ntua.gr:123456789/11723","is_oa":true,"landing_page_url":"http://doi.org/10.1090/S0025-5718-96-00718-1","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":"Mathematics of Computation","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00718-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00718-1","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00718-1/S0025-5718-96-00718-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2028157765.pdf","grobid_xml":"https://content.openalex.org/works/W2028157765.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W64179385","https://openalex.org/W71003253","https://openalex.org/W768639568","https://openalex.org/W1985494751","https://openalex.org/W2008542229","https://openalex.org/W2021048604","https://openalex.org/W2030155766","https://openalex.org/W2038430252","https://openalex.org/W2040679101","https://openalex.org/W2056195877","https://openalex.org/W2117088930","https://openalex.org/W2122436536","https://openalex.org/W2132260313","https://openalex.org/W2144144709","https://openalex.org/W2981569720","https://openalex.org/W3009340076","https://openalex.org/W3047743574","https://openalex.org/W3209416867","https://openalex.org/W4253305634"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2625833328"],"abstract_inverted_index":{"The":[0],"construction":[1],"of":[2,6,34,39,43,77,121,129,139,146,161,170,174,184,225,236,251,265,275],"a":[3,40,74,140,226,248,255,262],"Runge-Kutta":[4,189],"pair":[5,264],"order":[7,56,131,200],"<inline-formula":[8,44,59,83],"content-type=\"math/mathml\">":[9,45,60,84],"<mml:math":[10,46,61,85],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,47,62,86],"alttext=\"5":[12],"left-parenthesis":[13],"4":[14],"right-parenthesis\">":[15],"<mml:semantics>":[16,49,64,88],"<mml:mrow>":[17],"<mml:mn>5</mml:mn>":[18],"<mml:mo":[19,22],"stretchy=\"false\">(</mml:mo>":[20],"<mml:mn>4</mml:mn>":[21],"stretchy=\"false\">)</mml:mo>":[23],"</mml:mrow>":[24],"<mml:annotation":[25,51,66,90],"encoding=\"application/x-tex\">5(4)</mml:annotation>":[26],"</mml:semantics>":[27,53,68,92],"</mml:math>":[28,54,69,93],"</inline-formula>":[29,55,70,94],"with":[30,191,269],"the":[31,37,107,112,126,130,136,144,147,158,168,171,212,229,233,237,244,266],"minimal":[32],"number":[33],"stages":[35],"requires":[36],"solution":[38,149,160,169,224],"nonlinear":[41,175],"system":[42,128,173],"alttext=\"25\">":[48],"<mml:mn>25</mml:mn>":[50],"encoding=\"application/x-tex\">25</mml:annotation>":[52],"conditions":[57],"in":[58,182,218,258],"alttext=\"27\">":[63],"<mml:mn>27</mml:mn>":[65],"encoding=\"application/x-tex\">27</mml:annotation>":[67],"unknowns.":[71],"We":[72],"define":[73],"new":[75,245,267],"family":[76,268],"pairs":[78,81,103,190,208,246],"which":[79,104],"includes":[80],"using":[82,261],"alttext=\"6\">":[87],"<mml:mn>6</mml:mn>":[89],"encoding=\"application/x-tex\">6</mml:annotation>":[91],"function":[95,109],"evaluations":[96],"per":[97],"integration":[98],"step":[99],"as":[100,102],"well":[101],"additionally":[105],"use":[106,120],"first":[108],"evaluation":[110],"from":[111],"next":[113],"step.":[114],"This":[115],"is":[116,177,228],"achieved":[117],"by":[118,232,242],"making":[119],"Kutta\u2019s":[122],"simplifying":[123],"assumption":[124,213],"on":[125],"original":[127],"conditions,":[132],"i.e.,":[133],"that":[134,214],"all":[135],"internal":[137],"nodes":[138],"method":[141],"contributing":[142],"to":[143,157,193],"estimation":[145],"endpoint":[148],"provide,":[150],"at":[151],"these":[152],"nodes,":[153],"cost-free":[154],"second-order":[155],"approximations":[156],"true":[159],"any":[162],"differential":[163],"equation.":[164],"In":[165],"both":[166],"cases":[167],"resulting":[172],"equations":[176],"completely":[178],"classified":[179],"and":[180,201],"described":[181],"terms":[183],"five":[185],"free":[186],"parameters.":[187],"Optimal":[188],"respect":[192],"minimized":[194,270],"truncation":[195,271],"error":[196,272],"coefficients,":[197,273],"maximal":[198],"phase-lag":[199],"various":[202],"stability":[203],"characteristics":[204],"are":[205,216],"presented.":[206],"These":[207],"were":[209],"selected":[210],"under":[211],"they":[215],"used":[217],"Local":[219],"Extrapolation":[220],"Mode":[221],"(the":[222],"propagated":[223],"problem":[227],"one":[230],"provided":[231],"fifth-order":[234],"formula":[235],"pair).":[238],"Numerical":[239],"results":[240],"obtained":[241],"testing":[243],"over":[247],"standard":[249],"set":[250],"test":[252],"problems":[253],"suggest":[254],"significant":[256],"improvement":[257],"efficiency":[259],"when":[260],"specific":[263],"instead":[274],"some":[276],"other":[277],"existing":[278],"pairs.":[279]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}