{"id":"https://openalex.org/W2805205528","doi":"https://doi.org/10.9734/ajopacs/2018/40400","title":"Implicit Four Step Stormer-cowell-type Method for General Second Order Ordinary Differential Equations","display_name":"Implicit Four Step Stormer-cowell-type Method for General Second Order Ordinary Differential Equations","publication_year":2018,"publication_date":"2018-05-26","ids":{"openalex":"https://openalex.org/W2805205528","doi":"https://doi.org/10.9734/ajopacs/2018/40400","mag":"2805205528"},"language":"en","primary_location":{"id":"doi:10.9734/ajopacs/2018/40400","doi":"https://doi.org/10.9734/ajopacs/2018/40400","is_oa":true,"landing_page_url":"https://doi.org/10.9734/ajopacs/2018/40400","pdf_url":null,"source":{"id":"https://openalex.org/S4210209780","display_name":"Asian Journal of Physical and Chemical Sciences","issn_l":"2456-7779","issn":["2456-7779"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Journal of Physical and Chemical Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.9734/ajopacs/2018/40400","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"S Kayode","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I180664298","display_name":"Federal University of Technology","ror":"https://ror.org/01pvx8v81","country_code":"NG","type":"education","lineage":["https://openalex.org/I180664298"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"S Kayode","raw_affiliation_strings":["Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria","institution_ids":["https://openalex.org/I180664298"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112368087","display_name":"Olatunde Seun Ige","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I180664298","display_name":"Federal University of Technology","ror":"https://ror.org/01pvx8v81","country_code":"NG","type":"education","lineage":["https://openalex.org/I180664298"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"O Ige","raw_affiliation_strings":["Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria","institution_ids":["https://openalex.org/I180664298"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180664298"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06601326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"1","first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9965999722480774,"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 Solvers for Ordinary Differential Equations","score":0.9965999722480774,"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":0.0010999999940395355,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0005000000237487257,"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/second-order-ordinary-differential-equations","display_name":"second-order ordinary differential equations","score":0.9539999961853027},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.9599999785423279},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":1.0},{"id":"https://openalex.org/keywords/polynomial-basis","display_name":"polynomial basis","score":0.7129999995231628},{"id":"https://openalex.org/keywords/collocation-method","display_name":"collocation method","score":0.8159999847412109},{"id":"https://openalex.org/keywords/interpolation-formula","display_name":"interpolation formula","score":0.7070000171661377},{"id":"https://openalex.org/keywords/zero-stability","display_name":"zero stability","score":0.796999990940094},{"id":"https://openalex.org/keywords/consistency","display_name":"consistency","score":0.7279999852180481},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"numerical integration","score":0.39500001072883606}],"concepts":[{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7433454394340515},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6322852373123169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.552263081073761},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.4820731282234192},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47443878650665283},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.43831393122673035},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.42904362082481384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39592790603637695},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3408423066139221},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29497796297073364},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.18534493446350098},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.14303964376449585},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07208946347236633},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05854502320289612},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":3,"locations":[{"id":"doi:10.9734/ajopacs/2018/40400","doi":"https://doi.org/10.9734/ajopacs/2018/40400","is_oa":true,"landing_page_url":"https://doi.org/10.9734/ajopacs/2018/40400","pdf_url":null,"source":{"id":"https://openalex.org/S4210209780","display_name":"Asian Journal of Physical and Chemical Sciences","issn_l":"2456-7779","issn":["2456-7779"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Journal of Physical and Chemical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:journalajopacs.com:article/34","doi":null,"is_oa":true,"landing_page_url":"https://journalajopacs.com/index.php/AJOPACS/article/view/34","pdf_url":null,"source":{"id":"https://openalex.org/S4210209780","display_name":"Asian Journal of Physical and Chemical Sciences","issn_l":"2456-7779","issn":["2456-7779"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2456-7779","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-05370800v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05370800","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Asian Journal of Physical and Chemical Sciences, 2018, 6 (1), pp.1-10","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.9734/ajopacs/2018/40400","doi":"https://doi.org/10.9734/ajopacs/2018/40400","is_oa":true,"landing_page_url":"https://doi.org/10.9734/ajopacs/2018/40400","pdf_url":null,"source":{"id":"https://openalex.org/S4210209780","display_name":"Asian Journal of Physical and Chemical Sciences","issn_l":"2456-7779","issn":["2456-7779"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Journal of Physical and Chemical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2901640365","https://openalex.org/W2097041680","https://openalex.org/W7216489761","https://openalex.org/W1995249883","https://openalex.org/W7204497330","https://openalex.org/W2783169552","https://openalex.org/W2290408262","https://openalex.org/W2807609434","https://openalex.org/W2237650712","https://openalex.org/W2154887791"],"abstract_inverted_index":{"An":[0],"implicit":[1],"four":[2],"step":[3,103],"stormer-cowell-typed":[4],"method":[5,85,107],"for":[6,63],"direct":[7],"solution":[8,78],"of":[9,24,29,42,54,59,70,79,101],"general":[10],"second":[11],"order":[12],"ordinary":[13],"differential":[14],"equations":[15,46,60,94],"is":[16,108],"proposed":[17],"in":[18],"this":[19],"study.":[20],"In":[21],"the":[22,25,64,68,76,80,92,96,102,119],"derivation":[23],"method,":[26],"a":[27],"combination":[28],"chebyshev":[30],"and":[31,44,67,90,111],"legendre":[32],"polynomials":[33],"was":[34,61,86],"used":[35],"as":[36],"basis":[37,81],"function":[38],"to":[39,51],"generate":[40],"system":[41,58],"interpolation":[43],"collocation":[45],"at":[47,95],"selected":[48],"grid":[49,99],"points":[50],"obtain":[52],"systems":[53],"equation.":[55],"The":[56,83,105],"resulting":[57,93,106],"solved":[62],"unknown":[65],"parameters":[66,72],"values":[69],"these":[71],"were":[73],"substituted":[74],"into":[75],"approximate":[77],"function.":[82],"required":[84],"obtained":[87],"by":[88],"evaluating":[89],"simplify":[91],"last":[97],"end":[98],"point":[100],"number.":[104],"zero-stable,":[109],"consistent":[110],"normalized.":[112],"Numerical":[113],"results":[114],"compared":[115],"favourably":[116],"well":[117],"with":[118],"existing":[120],"methods.":[121]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2018-06-13T00:00:00"}