{"id":"https://openalex.org/W2085265038","doi":"https://doi.org/10.1080/00207160211933","title":"Parallel R-Point Explicit Block Method for Solving Second Order Ordinary Differential Equations Directly","display_name":"Parallel R-Point Explicit Block Method for Solving Second Order Ordinary Differential Equations Directly","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2085265038","doi":"https://doi.org/10.1080/00207160211933","mag":"2085265038"},"language":"en","primary_location":{"id":"doi:10.1080/00207160211933","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160211933","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/A5110218067","display_name":"Z. Omar","orcid":null},"institutions":[{"id":"https://openalex.org/I94625822","display_name":"Northern University of Malaysia","ror":"https://ror.org/01ss10648","country_code":"MY","type":"education","lineage":["https://openalex.org/I94625822"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Z. Omar","raw_affiliation_strings":["a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia"],"affiliations":[{"raw_affiliation_string":"a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","institution_ids":["https://openalex.org/I94625822"]},{"raw_affiliation_string":"a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103147179","display_name":"Muhammad Sulaiman","orcid":"https://orcid.org/0000-0002-4040-6211"},"institutions":[{"id":"https://openalex.org/I94625822","display_name":"Northern University of Malaysia","ror":"https://ror.org/01ss10648","country_code":"MY","type":"education","lineage":["https://openalex.org/I94625822"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"M. Sulaiman","raw_affiliation_strings":["a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia"],"affiliations":[{"raw_affiliation_string":"a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","institution_ids":["https://openalex.org/I94625822"]},{"raw_affiliation_string":"a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064797005","display_name":"M. Y. Saman","orcid":null},"institutions":[{"id":"https://openalex.org/I94625822","display_name":"Northern University of Malaysia","ror":"https://ror.org/01ss10648","country_code":"MY","type":"education","lineage":["https://openalex.org/I94625822"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"M. Y. Saman","raw_affiliation_strings":["a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia"],"affiliations":[{"raw_affiliation_string":"a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","institution_ids":["https://openalex.org/I94625822"]},{"raw_affiliation_string":"a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103518679","display_name":"D. J. Evans","orcid":null},"institutions":[{"id":"https://openalex.org/I94625822","display_name":"Northern University of Malaysia","ror":"https://ror.org/01ss10648","country_code":"MY","type":"education","lineage":["https://openalex.org/I94625822"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"D. J. Evans","raw_affiliation_strings":["a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia"],"affiliations":[{"raw_affiliation_string":"a   School of Information Technology , Universiti Utara Malaysia , Sintok Kedah,  Malaysia","institution_ids":["https://openalex.org/I94625822"]},{"raw_affiliation_string":"a School of Information Technology , Universiti Utara Malaysia , Sintok Kedah, Malaysia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110218067"],"corresponding_institution_ids":["https://openalex.org/I94625822"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.1863354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"79","issue":"3","first_page":"551","last_page":"560"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7538236379623413},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6803933382034302},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6364729404449463},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5446715354919434},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47364795207977295},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.4713681936264038},{"id":"https://openalex.org/keywords/explicit-and-implicit-methods","display_name":"Explicit and implicit methods","score":0.4619446396827698},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4577999413013458},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.4572851061820984},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4441237449645996},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4326499402523041},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3985349237918854},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.31753313541412354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2187252640724182},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11026185750961304},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08516433835029602}],"concepts":[{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7538236379623413},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6803933382034302},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6364729404449463},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5446715354919434},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47364795207977295},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.4713681936264038},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.4619446396827698},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4577999413013458},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.4572851061820984},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4441237449645996},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4326499402523041},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3985349237918854},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.31753313541412354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2187252640724182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11026185750961304},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08516433835029602}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00207160211933","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160211933","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:psasir.upm.edu.my:115363","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196260","display_name":"Universiti Putra Malaysia Institutional Repository (Universiti Putra Malaysia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130343225","host_organization_name":"Universiti Putra Malaysia","host_organization_lineage":["https://openalex.org/I130343225"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:irep.ntu.ac.uk:22453","is_oa":false,"landing_page_url":"http://irep.ntu.ac.uk/id/eprint/22453/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400559","display_name":"Nottingham Trent University's Institutional Repository (Nottingham Trent Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I52590639","host_organization_name":"Nottingham Trent University","host_organization_lineage":["https://openalex.org/I52590639"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1876990430","https://openalex.org/W2047993099","https://openalex.org/W2055032504","https://openalex.org/W2066490822","https://openalex.org/W2081953057","https://openalex.org/W2116054139","https://openalex.org/W2125580422","https://openalex.org/W2128938000","https://openalex.org/W2147662851","https://openalex.org/W2151807147","https://openalex.org/W2319973481"],"related_works":["https://openalex.org/W1990083358","https://openalex.org/W2918846270","https://openalex.org/W797453289","https://openalex.org/W643315884","https://openalex.org/W2341689988","https://openalex.org/W1193285027","https://openalex.org/W2060245387","https://openalex.org/W1498891866","https://openalex.org/W1983755086","https://openalex.org/W2803325358"],"abstract_inverted_index":{"A":[0],"new":[1,52,91],"parallel":[2,39,48,87],"R-point":[3],"explicit":[4],"block":[5],"method":[6,19,53,92],"for":[7,93],"solving":[8,94],"second":[9,95],"order":[10,96],"ordinary":[11],"differential":[12],"equations":[13,26],"(ODEs)":[14],"directly":[15,98],"is":[16],"developed.":[17],"The":[18,79],"computes":[20],"the":[21,25,36,45,51,55,64,70,82,86,90,101],"numerical":[22],"solution":[23],"of":[24,50,69,72,84,89],"at":[27],"three":[28],"points":[29],"simultaneously.":[30],"Each":[31],"problem":[32],"was":[33],"tested":[34],"on":[35],"shared":[37],"memory":[38],"computer":[40],"Sequent":[41],"S27":[42],"using":[43,85],"both":[44],"sequential":[46],"and":[47,54,76],"implementations":[49],"conventional":[56],"1-point":[57],"method.":[58],"Numerical":[59],"results":[60,80],"are":[61],"presented":[62],"comparing":[63],"two":[65],"methods":[66],"in":[67],"terms":[68],"number":[71],"steps":[73],"taken,":[74],"accuracy":[75],"execution":[77],"times.":[78],"indicate":[81],"advantages":[83],"implementation":[88],"ODEs":[97],"particularly":[99],"when":[100],"step":[102],"size":[103],"becomes":[104],"finer.":[105]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}