{"id":"https://openalex.org/W1995877011","doi":"https://doi.org/10.1080/00207169808804699","title":"Chebyshev solution for stiff delay differential equations","display_name":"Chebyshev solution for stiff delay differential equations","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1995877011","doi":"https://doi.org/10.1080/00207169808804699","mag":"1995877011"},"language":"en","primary_location":{"id":"doi:10.1080/00207169808804699","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804699","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/A5015114400","display_name":"A. El-Safty","orcid":"https://orcid.org/0000-0002-1504-6357"},"institutions":[{"id":"https://openalex.org/I91041137","display_name":"Assiut University","ror":"https://ror.org/01jaj8n65","country_code":"EG","type":"education","lineage":["https://openalex.org/I91041137"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"A. El-Safty","raw_affiliation_strings":["Department of Mathematics , Assiut University , Assiut, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Assiut University , Assiut, Egypt","institution_ids":["https://openalex.org/I91041137"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073381414","display_name":"M. A. Hussien","orcid":null},"institutions":[{"id":"https://openalex.org/I91041137","display_name":"Assiut University","ror":"https://ror.org/01jaj8n65","country_code":"EG","type":"education","lineage":["https://openalex.org/I91041137"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"M. A. Hussien","raw_affiliation_strings":["Department of Mathematics , Assiut University , Assiut, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Assiut University , Assiut, Egypt","institution_ids":["https://openalex.org/I91041137"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015114400"],"corresponding_institution_ids":["https://openalex.org/I91041137"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.14798003,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"3-4","first_page":"323","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9901999831199646,"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":0.9901999831199646,"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":0.9485999941825867,"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"}},{"id":"https://openalex.org/T12898","display_name":"Induction Heating and Inverter Technology","score":0.9266999959945679,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/delay-differential-equation","display_name":"Delay differential equation","score":0.7260435223579407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7124699950218201},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5981460213661194},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.5474255681037903},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.5258786678314209},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5070645809173584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4422960877418518},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.4406314492225647},{"id":"https://openalex.org/keywords/l-stability","display_name":"L-stability","score":0.419512540102005},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.4158147871494293},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.39956384897232056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3873496651649475},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.205041766166687},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.18171584606170654},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.05764627456665039}],"concepts":[{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.7260435223579407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7124699950218201},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5981460213661194},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.5474255681037903},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.5258786678314209},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5070645809173584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4422960877418518},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4406314492225647},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.419512540102005},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.4158147871494293},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.39956384897232056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3873496651649475},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.205041766166687},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.18171584606170654},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.05764627456665039},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169808804699","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804699","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":[{"id":"https://openalex.org/F4320325647","display_name":"Assiut University","ror":"https://ror.org/01jaj8n65"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W9946612","https://openalex.org/W99790034","https://openalex.org/W1555459452","https://openalex.org/W1972574198","https://openalex.org/W2019230842","https://openalex.org/W2032936023","https://openalex.org/W2094250736","https://openalex.org/W2151807147","https://openalex.org/W2318788438","https://openalex.org/W3023467406"],"related_works":["https://openalex.org/W2112919228","https://openalex.org/W1585782015","https://openalex.org/W2136992695","https://openalex.org/W1512440940","https://openalex.org/W2039550572","https://openalex.org/W2021099221","https://openalex.org/W2054912819","https://openalex.org/W2089969332","https://openalex.org/W2021023807","https://openalex.org/W2588042187"],"abstract_inverted_index":{"A":[0],"method":[1,25],"based":[2],"on":[3],"El-Gendi":[4],"[1974],":[5],"is":[6],"given":[7],"for":[8],"the":[9,19],"numerical":[10],"solution":[11],"of":[12,21,32],"stiff":[13,30],"delay":[14,36],"differential":[15],"equations":[16],"(DDES)":[17,33],"in":[18],"form":[20],"Chebyshev":[22],"series.":[23],"The":[24],"can":[26],"be":[27],"applied":[28],"to":[29],"system":[31],"with":[34,40],"single":[35],"as":[37],"well":[38],"as,":[39],"several":[41],"delays.":[42],"Numerical":[43],"examples":[44],"are":[45],"given.":[46]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}