{"id":"https://openalex.org/W3135552027","doi":"https://doi.org/10.1080/00207160.2021.1900567","title":"Collocation Runge\u2013Kutta\u2013Nystr\u00f6m methods for solving second-order initial value problems","display_name":"Collocation Runge\u2013Kutta\u2013Nystr\u00f6m methods for solving second-order initial value problems","publication_year":2021,"publication_date":"2021-03-09","ids":{"openalex":"https://openalex.org/W3135552027","doi":"https://doi.org/10.1080/00207160.2021.1900567","mag":"3135552027"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2021.1900567","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1900567","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5111423364","display_name":"N. S. Hoang","orcid":null},"institutions":[{"id":"https://openalex.org/I5950314","display_name":"University of West Georgia","ror":"https://ror.org/01cqxk816","country_code":"US","type":"education","lineage":["https://openalex.org/I5950314"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"N. S. Hoang","raw_affiliation_strings":["Department of Mathematics, University of West Georgia, Carrollton, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of West Georgia, Carrollton, GA, USA","institution_ids":["https://openalex.org/I5950314"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111423364"],"corresponding_institution_ids":["https://openalex.org/I5950314"],"apc_list":null,"apc_paid":null,"fwci":1.1783,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73434343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"98","issue":"12","first_page":"2423","last_page":"2444"},"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":0.9991999864578247,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.8584489226341248},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.7464359998703003},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7281625866889954},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7135925889015198},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.7041072845458984},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6815545558929443},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5660426616668701},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5285122394561768},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4929165840148926},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4730491042137146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47153550386428833},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45764845609664917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.433003693819046},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.3754119277000427},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.27812790870666504},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13806158304214478},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.07212704420089722},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0627484917640686}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8584489226341248},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.7464359998703003},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7281625866889954},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7135925889015198},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7041072845458984},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6815545558929443},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5660426616668701},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5285122394561768},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4929165840148926},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4730491042137146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47153550386428833},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45764845609664917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.433003693819046},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3754119277000427},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.27812790870666504},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13806158304214478},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.07212704420089722},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0627484917640686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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:10.1080/00207160.2021.1900567","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1900567","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1509923322","https://openalex.org/W1543750907","https://openalex.org/W1972279567","https://openalex.org/W1983256552","https://openalex.org/W1989691897","https://openalex.org/W1997933267","https://openalex.org/W2013291190","https://openalex.org/W2022175921","https://openalex.org/W2023344463","https://openalex.org/W2071225300","https://openalex.org/W2081103269","https://openalex.org/W2091032504","https://openalex.org/W3209416867"],"related_works":["https://openalex.org/W2045953892","https://openalex.org/W1843663759","https://openalex.org/W2031484768","https://openalex.org/W4384829779","https://openalex.org/W2032662168","https://openalex.org/W2765372099","https://openalex.org/W2363361243","https://openalex.org/W3126297227","https://openalex.org/W2384941625","https://openalex.org/W2162080230"],"abstract_inverted_index":{"A":[0],"class":[1,33],"of":[2,34,70,86,89,96,115,132],"modified":[3,81,117],"collocation":[4,43,71,82,97],"Runge\u2013Kutta\u2013Nystr\u00f6m":[5],"(RKN)":[6],"methods":[7,27,45,52,64,119],"for":[8,61,93],"solving":[9],"second-order":[10,35],"initial":[11,36],"value":[12,37],"problem":[13],"y\u2033=f(t,y,y\u2032),":[14],"y(t0)=y0,":[15],"y\u2032(t0)=y0\u2032":[16],"has":[17],"been":[18,122],"formulated":[19],"and":[20,46,100,112],"studied":[21],"in":[22],"the":[23,41,50,58,62,68,113,130,133],"paper.":[24],"The":[25,109],"new":[26,63,134],"are":[28,106,126],"applicable":[29],"to":[30,40,49,128],"a":[31],"larger":[32],"problems":[38],"compared":[39],"classical":[42,51],"RKN":[44,83,118],"they":[47],"reduce":[48],"when":[53,67,104],"y\u2032":[54],"is":[55,65,85],"absent":[56],"from":[57],"equation.":[59],"Superconvergence":[60],"attained":[66],"set":[69,95],"points":[72],"satisfies":[73],"orthogonality":[74],"conditions.":[75],"We":[76],"proved":[77],"that":[78],"an":[79],"s-stage":[80],"method":[84],"accuracy":[87],"order":[88],"at":[90,101],"least":[91],"s":[92],"any":[94],"parameters":[98],"c":[99,105],"most":[102],"2s":[103],"Gauss":[107],"points.":[108],"stability":[110,114],"function":[111],"some":[116],"have":[120],"also":[121],"investigated.":[123],"Numerical":[124],"experiments":[125],"included":[127],"demonstrate":[129],"advantage":[131],"methods.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}