{"id":"https://openalex.org/W2149089017","doi":"https://doi.org/10.1080/00207160310001614963","title":"A computational method for the equal width equation","display_name":"A computational method for the equal width equation","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2149089017","doi":"https://doi.org/10.1080/00207160310001614963","mag":"2149089017"},"language":"en","primary_location":{"id":"doi:10.1080/00207160310001614963","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160310001614963","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/A5040768839","display_name":"K. R. Raslan","orcid":"https://orcid.org/0000-0001-7631-4071"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"K. R. Raslan","raw_affiliation_strings":["a  Al-Azhar University,  Department of Mathematics, Faculty of Science  , Nasr-City,  11884 ,  Cairo ,  Egypt"],"affiliations":[{"raw_affiliation_string":"a  Al-Azhar University,  Department of Mathematics, Faculty of Science  , Nasr-City,  11884 ,  Cairo ,  Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040768839"],"corresponding_institution_ids":["https://openalex.org/I184834183"],"apc_list":null,"apc_paid":null,"fwci":4.5596,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94169021,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"81","issue":"1","first_page":"63","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9937999844551086,"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/T12233","display_name":"Geotechnical Engineering and Underground Structures","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematics","display_name":"Mathematics","score":0.8401022553443909},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.7132375836372375},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6309725046157837},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6151160597801208},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.5936216711997986},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.579282820224762},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5259727835655212},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.48859506845474243},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4779224991798401},{"id":"https://openalex.org/keywords/b-spline","display_name":"B-spline","score":0.46341365575790405},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44953256845474243},{"id":"https://openalex.org/keywords/stiff-equation","display_name":"Stiff equation","score":0.4303346276283264},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3317604660987854},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12149566411972046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0765831470489502}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8401022553443909},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.7132375836372375},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6309725046157837},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6151160597801208},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.5936216711997986},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.579282820224762},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5259727835655212},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.48859506845474243},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4779224991798401},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.46341365575790405},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44953256845474243},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.4303346276283264},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3317604660987854},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12149566411972046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0765831470489502},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160310001614963","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160310001614963","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:CiteSeerX.psu:10.1.1.99.770","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.770","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://docs.ksu.edu.sa/PDF/Articles09/Article090155.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1969449454","https://openalex.org/W2035310520","https://openalex.org/W2040355399","https://openalex.org/W2044804236","https://openalex.org/W2077464783","https://openalex.org/W2087746595"],"related_works":["https://openalex.org/W1562832873","https://openalex.org/W1843663759","https://openalex.org/W1972583070","https://openalex.org/W4226207752","https://openalex.org/W2384941625","https://openalex.org/W2132514189","https://openalex.org/W2241327589","https://openalex.org/W2071225300","https://openalex.org/W2373327722","https://openalex.org/W2030196497"],"abstract_inverted_index":{"A":[0],"B-spline":[1],"finite":[2,51],"element":[3,28],"method":[4,19],"is":[5,40,61,76],"used":[6,70,78],"to":[7,65,71,79],"solve":[8],"the":[9,24,33,43,50,54,73,81],"equal":[10],"width":[11],"equation":[12],"numerically.":[13],"This":[14],"approach":[15],"involves":[16],"a":[17],"collocation":[18],"using":[20,42],"quintic":[21],"B-splines":[22],"at":[23],"knot":[25],"points":[26],"as":[27],"shape.":[29],"Time":[30],"integration":[31],"of":[32,36,49,57,84],"resulting":[34,55],"system":[35,56],"ordinary":[37,58],"differential":[38,59],"equations":[39,60],"effected":[41],"fourth":[44],"order":[45],"Runge\u2013Kutta":[46],"method,":[47,53],"instead":[48],"difference":[52],"integrated":[62],"with":[63],"respect":[64],"time.":[66],"Standard":[67],"problems":[68],"are":[69],"validate":[72],"algorithm":[74],"which":[75],"then":[77],"model":[80],"smooth":[82],"development":[83],"an":[85],"undular":[86],"bore.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
