{"id":"https://openalex.org/W7131900982","doi":"https://doi.org/10.1134/s1995423925700016","title":"Explicit Two-Derivative Runge\u2013Kutta Methods Coupled with the Richardson Extrapolation","display_name":"Explicit Two-Derivative Runge\u2013Kutta Methods Coupled with the Richardson Extrapolation","publication_year":2025,"publication_date":"2025-12-01","ids":{"openalex":"https://openalex.org/W7131900982","doi":"https://doi.org/10.1134/s1995423925700016"},"language":"en","primary_location":{"id":"doi:10.1134/s1995423925700016","doi":"https://doi.org/10.1134/s1995423925700016","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995423925700016","pdf_url":null,"source":{"id":"https://openalex.org/S2259906","display_name":"Numerical Analysis and Applications","issn_l":"1560-7526","issn":["1560-7526","1995-4239","1995-4247"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-1","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Analysis and Applications","raw_type":"journal-article"},"volume":null,"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/A5094101468","display_name":"Mozhgan Eghbaljoo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Eghbaljoo","raw_affiliation_strings":["Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080290364","display_name":"Gholamreza Hojjati","orcid":"https://orcid.org/0000-0001-8406-763X","observed_orcids":["https://orcid.org/0000-0001-8406-763X"]},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"G. Hojjati","raw_affiliation_strings":["Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":null,"display_name":"A. Abdi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"A. Abdi","raw_affiliation_strings":["Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084332938","display_name":"Pari Khakzad","orcid":"https://orcid.org/0000-0001-5012-4990","observed_orcids":["https://orcid.org/0000-0001-5012-4990"]},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"P. Khakzad","raw_affiliation_strings":["Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080290364"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":null,"apc_paid":null,"fwci":1.0321,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79323513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"18","issue":"4","first_page":"351","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"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":0.9990000128746033,"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/T11191","display_name":"Mathematical functions and polynomials","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":9.999999747378752e-05,"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/richardson-extrapolation","display_name":"Richardson extrapolation","score":0.9950000047683716},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.7110000252723694},{"id":"https://openalex.org/keywords/numerical-accuracy","display_name":"numerical accuracy","score":0.625},{"id":"https://openalex.org/keywords/numerical-integration-of-odes","display_name":"numerical integration of ODEs","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C102893441","wikidata":"https://www.wikidata.org/wiki/Q1063089","display_name":"Richardson extrapolation","level":3,"score":0.9017000198364258},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.8378000259399414},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.6990000009536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6966000199317932},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6834999918937683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5683000087738037},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.545199990272522},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.48579999804496765},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4205000102519989},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.39730000495910645},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3628000020980835},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.35269999504089355},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33649998903274536},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.3095000088214874},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.2815000116825104},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C2986605239","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Numerical models","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C136798861","wikidata":"https://www.wikidata.org/wiki/Q1826712","display_name":"Method of lines","level":5,"score":0.25360000133514404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s1995423925700016","doi":"https://doi.org/10.1134/s1995423925700016","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995423925700016","pdf_url":null,"source":{"id":"https://openalex.org/S2259906","display_name":"Numerical Analysis and Applications","issn_l":"1560-7526","issn":["1560-7526","1995-4239","1995-4247"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-1","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1964070472","https://openalex.org/W1980266375","https://openalex.org/W1994600466","https://openalex.org/W1995922787","https://openalex.org/W1996574028","https://openalex.org/W2054313441","https://openalex.org/W2057998877","https://openalex.org/W2068073951","https://openalex.org/W2075866208","https://openalex.org/W2076047216","https://openalex.org/W2076641549","https://openalex.org/W2085917197","https://openalex.org/W2088116518","https://openalex.org/W2329721603","https://openalex.org/W2600168676","https://openalex.org/W2963886023","https://openalex.org/W3022526523","https://openalex.org/W3042789352","https://openalex.org/W3106986181","https://openalex.org/W3165874937","https://openalex.org/W3186026530","https://openalex.org/W3215133951","https://openalex.org/W4283169473","https://openalex.org/W4324387102"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1,57],"aim":[2],"of":[3,16,30,40,52,70],"this":[4,41],"paper":[5],"is":[6],"to":[7,27],"derive":[8],"efficient":[9],"numerical":[10,14,55,72],"algorithms":[11,63],"for":[12,60],"the":[13,23,47,53,61,68],"solution":[15],"nonstiff":[17],"ordinary":[18],"differential":[19],"equations":[20],"by":[21,67],"applying":[22],"Richardson":[24],"extrapolation":[25],"technique":[26,42],"a":[28],"class":[29],"explicit":[31],"two-derivative":[32],"Runge\u2013Kutta":[33],"methods.":[34,56],"Theoretical":[35],"results":[36,69],"illustrate":[37],"that":[38],"application":[39],"has":[43],"considerable":[44],"impact":[45],"on":[46],"accuracy":[48],"and":[49],"stability":[50],"properties":[51],"underlying":[54],"achieved":[58],"improvements":[59],"proposed":[62],"are":[64],"also":[65],"confirmed":[66],"some":[71],"experiments.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-02-28T00:00:00"}