{"id":"https://openalex.org/W2063558383","doi":"https://doi.org/10.1080/00207160601084505","title":"Embedded implicit Runge\u2013Kutta Nystr\u00f6m method for solving second-order differential equations","display_name":"Embedded implicit Runge\u2013Kutta Nystr\u00f6m method for solving second-order differential equations","publication_year":2006,"publication_date":"2006-11-01","ids":{"openalex":"https://openalex.org/W2063558383","doi":"https://doi.org/10.1080/00207160601084505","mag":"2063558383"},"language":"en","primary_location":{"id":"doi:10.1080/00207160601084505","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160601084505","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/A5082737142","display_name":"S. O. Imoni","orcid":null},"institutions":[{"id":"https://openalex.org/I28653996","display_name":"Adekunle Ajasin University","ror":"https://ror.org/04e27p903","country_code":"NG","type":"education","lineage":["https://openalex.org/I28653996"]}],"countries":["NG"],"is_corresponding":true,"raw_author_name":"S. O. Imoni","raw_affiliation_strings":["\n Department of Industrial Mathematics, Adekunle Ajasin University, P.M.B. 001 Akungba-Akoko, Ondo State, Nigeria","Department of Industrial Mathematics , Adekunle Ajasin University , P.M.B. 001 Akungba-Akoko, Ondo State, Nigeria"],"affiliations":[{"raw_affiliation_string":"\n Department of Industrial Mathematics, Adekunle Ajasin University, P.M.B. 001 Akungba-Akoko, Ondo State, Nigeria","institution_ids":["https://openalex.org/I28653996"]},{"raw_affiliation_string":"Department of Industrial Mathematics , Adekunle Ajasin University , P.M.B. 001 Akungba-Akoko, Ondo State, Nigeria","institution_ids":["https://openalex.org/I28653996"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063348836","display_name":"F. O. Otunta","orcid":null},"institutions":[{"id":"https://openalex.org/I6406202","display_name":"University of Benin","ror":"https://ror.org/04mznrw11","country_code":"NG","type":"education","lineage":["https://openalex.org/I6406202"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"F. O. Otunta","raw_affiliation_strings":["\n Department of Mathematics, University of Benin, P.M.B 1154, Benin City, Nigeria","Department of Mathematics , University of Benin , P.M.B 1154, Benin City, Nigeria"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, University of Benin, P.M.B 1154, Benin City, Nigeria","institution_ids":["https://openalex.org/I6406202"]},{"raw_affiliation_string":"Department of Mathematics , University of Benin , P.M.B 1154, Benin City, Nigeria","institution_ids":["https://openalex.org/I6406202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073268546","display_name":"T. R. Ramamohan","orcid":"https://orcid.org/0009-0009-6607-3214"},"institutions":[{"id":"https://openalex.org/I2799463389","display_name":"Fourth Paradigm Institute","ror":"https://ror.org/03n73vq73","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I2799463389","https://openalex.org/I4210134808","https://openalex.org/I66760702"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"T. R. Ramamohan","raw_affiliation_strings":["\n CSIR-Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore, 560 037, India","CSIR Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore 560 037, India"],"affiliations":[{"raw_affiliation_string":"\n CSIR-Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore, 560 037, India","institution_ids":["https://openalex.org/I2799463389"]},{"raw_affiliation_string":"CSIR Centre for Mathematical Modelling and Computer Simulation, NAL Belur Campus, Bangalore 560 037, India","institution_ids":["https://openalex.org/I2799463389"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082737142"],"corresponding_institution_ids":["https://openalex.org/I28653996"],"apc_list":null,"apc_paid":null,"fwci":0.4526,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.65021192,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"83","issue":"11","first_page":"777","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9973999857902527,"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":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.9214503765106201},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.743567705154419},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6420974731445312},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5934739708900452},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5708577632904053},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5154767632484436},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.504719614982605},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5027105808258057},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.4825853109359741},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.4746161997318268},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45365726947784424},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4491916000843048},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.42900437116622925},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4246675968170166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.350394070148468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1669495403766632},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.1619407832622528},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14878630638122559},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08539131283760071}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9214503765106201},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.743567705154419},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6420974731445312},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5934739708900452},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5708577632904053},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5154767632484436},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.504719614982605},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5027105808258057},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4825853109359741},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.4746161997318268},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45365726947784424},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4491916000843048},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.42900437116622925},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4246675968170166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.350394070148468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1669495403766632},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.1619407832622528},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14878630638122559},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08539131283760071},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160601084505","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160601084505","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:nal-ir.nal.res.in:8902","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401046","display_name":"Institutional Repository @ NAL (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320721","display_name":"Council of Scientific and Industrial Research, India","ror":"https://ror.org/021wm7p51"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W219694864","https://openalex.org/W1989790212","https://openalex.org/W1989897441","https://openalex.org/W2019084245","https://openalex.org/W2020345874","https://openalex.org/W2030224870","https://openalex.org/W2038200431","https://openalex.org/W2042388195","https://openalex.org/W2050666969","https://openalex.org/W2067221458","https://openalex.org/W2126340238","https://openalex.org/W2129081409","https://openalex.org/W2167514055"],"related_works":["https://openalex.org/W138907054","https://openalex.org/W21086365","https://openalex.org/W2052381424","https://openalex.org/W2160716572","https://openalex.org/W2006038957","https://openalex.org/W2030109199","https://openalex.org/W4317934108","https://openalex.org/W2223041667","https://openalex.org/W109678862","https://openalex.org/W1995438682"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"a":[3],"new":[4,73],"embedded":[5],"Singly":[6],"Diagonally":[7],"Implicit":[8],"Runge-Kutta":[9,64],"Nystrom":[10],"fourth":[11],"order":[12,15,21,55],"in":[13],"fifth":[14],"method":[16],"for":[17],"solving":[18],"special":[19],"second":[20],"initial":[22],"value":[23],"problems":[24,32,50],"is":[25],"derived.":[26],"A":[27],"standard":[28],"set":[29,47],"of":[30,48,71],"test":[31,49],"are":[33,42,51],"tested":[34],"upon":[35],"and":[36,57],"comparisons":[37],"on":[38],"the":[39,45,60,69,72],"numerical":[40],"results":[41,67],"made":[43],"when":[44],"same":[46],"reduced":[52],"to":[53],"first":[54],"systems":[56],"solved":[58],"using":[59],"existingembedded":[61],"diagonally":[62],"implicit":[63],"method.":[65,74],"The":[66],"suggests":[68],"superiority":[70]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}