{"id":"https://openalex.org/W2185961187","doi":"https://doi.org/10.12816/0004797","title":"Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem","display_name":"Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2185961187","doi":"https://doi.org/10.12816/0004797","mag":"2185961187"},"language":"en","primary_location":{"id":"doi:10.12816/0004797","doi":"https://doi.org/10.12816/0004797","is_oa":false,"landing_page_url":"https://doi.org/10.12816/0004797","pdf_url":null,"source":{"id":"https://openalex.org/S4210220220","display_name":"Journal of Engineering and Applied Sciences","issn_l":"1658-6638","issn":["1658-6638","1658-7073"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Engineering and Applied Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5001991582","display_name":"M. El-Kady","orcid":"https://orcid.org/0000-0002-4644-6804","observed_orcids":["https://orcid.org/0000-0002-4644-6804"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. El-Kady","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101689820","display_name":"Mohamed A. Attia","orcid":"https://orcid.org/0000-0002-6485-9880","observed_orcids":["https://orcid.org/0000-0002-6485-9880"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M.A.Attia M.A.Attia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"F. Ragab","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Ragab","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"37","last_page":"43"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.5048999786376953,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.5048999786376953,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.14030000567436218,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.10239999741315842,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/beam-bending","display_name":"beam bending","score":0.8140000104904175},{"id":"https://openalex.org/keywords/fourth-order-boundary-value-problems","display_name":"fourth-order boundary value problems","score":0.7900000214576721},{"id":"https://openalex.org/keywords/rectangular-beams","display_name":"rectangular beams","score":0.6859999895095825},{"id":"https://openalex.org/keywords/elastic-foundation","display_name":"elastic foundation","score":0.9940000176429749},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"nonlinear programming","score":0.8029999732971191}],"concepts":[{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.6338357925415039},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.624297559261322},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.574122428894043},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.5718254446983337},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5388111472129822},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.5023407936096191},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.49991512298583984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4986100196838379},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4882505238056183},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4518461227416992},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.44774726033210754},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43589872121810913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4146583378314972},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.16269689798355103},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.1448880136013031},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11463433504104614},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.07003572583198547},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0635528564453125},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.12816/0004797","doi":"https://doi.org/10.12816/0004797","is_oa":false,"landing_page_url":"https://doi.org/10.12816/0004797","pdf_url":null,"source":{"id":"https://openalex.org/S4210220220","display_name":"Journal of Engineering and Applied Sciences","issn_l":"1658-6638","issn":["1658-6638","1658-7073"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Engineering and Applied Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W148815461","https://openalex.org/W1535869933","https://openalex.org/W2004937620","https://openalex.org/W2014513898","https://openalex.org/W2051570923","https://openalex.org/W2056882255","https://openalex.org/W2058345382","https://openalex.org/W2074531724","https://openalex.org/W3038165843"],"related_works":["https://openalex.org/W4403976516","https://openalex.org/W2549790548","https://openalex.org/W2900666889","https://openalex.org/W2750536820","https://openalex.org/W2035254670","https://openalex.org/W2055208363","https://openalex.org/W2156785040","https://openalex.org/W2773003736","https://openalex.org/W2546270417","https://openalex.org/W2063292039"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,we":[2],"applied":[3],"successive":[4],"ultraspherical":[5],"integration":[6,50],"matrices,":[7],"which":[8],"are":[9],"used":[10,35],"for":[11,38],"the":[12,39,46,52,59,63,83],"numerical":[13],"solution":[14],"of":[15,25,51,65,82],"fourth":[16],"order":[17],"linear":[18],"boundary":[19],"value":[20],"problem":[21],"arising":[22],"in":[23,62],"bending":[24],"a":[26],"rectangular":[27],"beam":[28],"on":[29],"elastic":[30],"foundation.":[31],"This":[32],"method":[33,85],"is":[34,71],"to":[36,45,73],"approximate":[37],"highest-order":[40,53],"derivative":[41],"and":[42,68,80],"generating":[43],"approximations":[44],"lower-order":[47],"derivatives":[48],"through":[49],"derivative.":[54],"We":[55],"can":[56],"then":[57],"use":[58],"produced":[60],"equations":[61],"form":[64],"algebraic":[66],"system":[67],"hence":[69],"it":[70],"converted":[72],"nonlinear":[74],"programming.":[75],"Numerical":[76],"examples":[77],"illustratedthe":[78],"accuracy":[79],"efficiency":[81],"proposed":[84]},"counts_by_year":[{"year":2021,"cited_by_count":3}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2016-06-24T00:00:00"}
