{"id":"https://openalex.org/W2025831716","doi":"https://doi.org/10.1080/00207169108804006","title":"A modified numerov integration method for general second order initial value Problems","display_name":"A modified numerov integration method for general second order initial value Problems","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2025831716","doi":"https://doi.org/10.1080/00207169108804006","mag":"2025831716"},"language":"en","primary_location":{"id":"doi:10.1080/00207169108804006","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169108804006","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/A5088494720","display_name":"Maarten Van Daele","orcid":"https://orcid.org/0000-0002-8530-4438"},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"M. Van Daele","raw_affiliation_strings":["\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109967168","display_name":"H. De Meyer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. De Meyer","raw_affiliation_strings":["\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036599342","display_name":"G. Vanden Berghe","orcid":"https://orcid.org/0000-0002-7215-9446"},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"G. Vanden Berghe","raw_affiliation_strings":["\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium"],"affiliations":[{"raw_affiliation_string":"\n                   \n               Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent, Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica Rijksuniversiteit-Gent , Krijgslaan-281-S9, Gent, B9000, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088494720"],"corresponding_institution_ids":["https://openalex.org/I4210142349"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.18507973,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"1-2","first_page":"117","last_page":"127"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987999796867371,"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":0.9952999949455261,"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/order","display_name":"Order (exchange)","score":0.7026814818382263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6067906618118286},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5745073556900024},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5628376007080078},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5098461508750916},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.508600115776062},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.4729442596435547},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.4640144109725952},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4289345443248749},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.42542874813079834},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30479490756988525},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27249109745025635},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.20402780175209045},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.1278391182422638},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09379193186759949}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.7026814818382263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6067906618118286},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5745073556900024},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5628376007080078},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5098461508750916},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.508600115776062},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.4729442596435547},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.4640144109725952},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4289345443248749},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42542874813079834},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30479490756988525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27249109745025635},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.20402780175209045},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.1278391182422638},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09379193186759949},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169108804006","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169108804006","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2029252791","https://openalex.org/W2034951064","https://openalex.org/W2109537209","https://openalex.org/W2142821382","https://openalex.org/W2149109834","https://openalex.org/W2151207784","https://openalex.org/W2211924474"],"related_works":["https://openalex.org/W53239147","https://openalex.org/W2092244978","https://openalex.org/W2361296752","https://openalex.org/W2254834887","https://openalex.org/W1994753406","https://openalex.org/W2480921170","https://openalex.org/W3217220159","https://openalex.org/W2015745036","https://openalex.org/W2389611137","https://openalex.org/W2030671289"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"an":[3,50],"implicit":[4],"eighth-order":[5],"finite":[6],"difference":[7],"method":[8,27],"for":[9,81,92,104],"the":[10,20,42,78,89,101],"general":[11],"second":[12,68],"order":[13,69],"non-linear":[14],"differential":[15],"equation":[16],"Yn=f(t,y,y)":[17],"subject":[18],"to":[19,40,49,61],"initial":[21,70],"conditions":[22],"y(to)":[23],"=yo,":[24],"y(to)=yO.":[25],"The":[26,44],"is":[28],"based":[29],"on":[30],"mixed":[31],"interpolation":[32],"containing":[33],"a":[34],"parameter":[35],"which":[36],"can":[37],"be":[38],"used":[39],"improve":[41],"accuracy.":[43],"same":[45],"technique":[46],"gives":[47],"rise":[48],"explicit":[51],"sixth-order":[52],"integration":[53],"scheme.":[54],"Numerical":[55],"solutions":[56],"of":[57],"problems":[58],"are":[59],"given":[60],"illustrate":[62],"both":[63],"methods.":[64],"Keywords:":[65],"Numerov":[66],"methodnon-linear":[67],"value":[71],"problemsC.R.":[72],"Categories:":[73],"G.1.7G.1.0":[74],"\u2217Research":[75,86,98],"Director":[76,87,99],"at":[77,88,100],"National":[79,90,102],"Fund":[80,91,103],"Scientific":[82,93,105],"Research":[83,94,106],"(N.F.W.O.":[84,95,107],"Belgium).":[85,96,108],"Notes":[97]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}