{"id":"https://openalex.org/W4366278967","doi":"https://doi.org/10.3390/sym15040931","title":"Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique","display_name":"Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique","publication_year":2023,"publication_date":"2023-04-18","ids":{"openalex":"https://openalex.org/W4366278967","doi":"https://doi.org/10.3390/sym15040931"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040931","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040931","pdf_url":"https://www.mdpi.com/2073-8994/15/4/931/pdf?version=1681808915","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/931/pdf?version=1681808915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040573430","display_name":"Mohamed Adel","orcid":"https://orcid.org/0000-0001-7069-697X"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]},{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Mohamed Adel","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt","Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-7069-697X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017801061","display_name":"M. M. Khader","orcid":"https://orcid.org/0000-0003-3844-139X"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]},{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mohamed M. Khader","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia","Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-3844-139X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087432269","display_name":"Taghreed A. Assiri","orcid":"https://orcid.org/0000-0003-3911-784X"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Taghreed A. Assiri","raw_affiliation_strings":["Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026223294","display_name":"Wajdi Kallel","orcid":null},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Wajdi Kallel","raw_affiliation_strings":["Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5040573430"],"corresponding_institution_ids":["https://openalex.org/I145487455","https://openalex.org/I4210151290"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.8682,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90801784,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"931","last_page":"931"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":"Differential Equations and Numerical Methods","score":0.9442999958992004,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.638957142829895},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5970775485038757},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5943654775619507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.54245525598526},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4860861599445343},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.47623518109321594},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4725085198879242},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46965375542640686},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4446165859699249},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44039052724838257},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4181879758834839},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4176216721534729},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3770706057548523},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3503449559211731},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19759094715118408},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15009641647338867},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08072918653488159}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.638957142829895},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5970775485038757},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5943654775619507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.54245525598526},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4860861599445343},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.47623518109321594},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4725085198879242},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46965375542640686},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4446165859699249},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44039052724838257},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4181879758834839},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4176216721534729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3770706057548523},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3503449559211731},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19759094715118408},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15009641647338867},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08072918653488159},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"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/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040931","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040931","pdf_url":"https://www.mdpi.com/2073-8994/15/4/931/pdf?version=1681808915","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7d89d8f9411e4faaa45497485ac9a41e","is_oa":false,"landing_page_url":"https://doaj.org/article/7d89d8f9411e4faaa45497485ac9a41e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 931 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/931/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040931","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040931","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040931","pdf_url":"https://www.mdpi.com/2073-8994/15/4/931/pdf?version=1681808915","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4366278967.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W101171454","https://openalex.org/W1490180844","https://openalex.org/W1978610735","https://openalex.org/W2000564937","https://openalex.org/W2022436731","https://openalex.org/W2022664105","https://openalex.org/W2041572706","https://openalex.org/W2064893412","https://openalex.org/W2080456722","https://openalex.org/W2101423148","https://openalex.org/W2200387372","https://openalex.org/W2780637467","https://openalex.org/W2790210339","https://openalex.org/W2790315580","https://openalex.org/W2908376761","https://openalex.org/W2913984069","https://openalex.org/W3011427855","https://openalex.org/W3024738577","https://openalex.org/W3031197895","https://openalex.org/W3087469952","https://openalex.org/W3091776190","https://openalex.org/W3094573482","https://openalex.org/W3120252076","https://openalex.org/W3162033558","https://openalex.org/W3172249873","https://openalex.org/W3192906354","https://openalex.org/W3207850185","https://openalex.org/W4200493171","https://openalex.org/W4281670910","https://openalex.org/W4282917304","https://openalex.org/W4283576870","https://openalex.org/W4284697030","https://openalex.org/W4298060601","https://openalex.org/W4311717527","https://openalex.org/W4312851570","https://openalex.org/W4317608847","https://openalex.org/W4318833176","https://openalex.org/W6640011337","https://openalex.org/W6784835780","https://openalex.org/W6795782427"],"related_works":["https://openalex.org/W2938514635","https://openalex.org/W4360764540","https://openalex.org/W4231657010","https://openalex.org/W2007917622","https://openalex.org/W1994552539","https://openalex.org/W2385305544","https://openalex.org/W1550587116","https://openalex.org/W2118018204","https://openalex.org/W2212647145","https://openalex.org/W2402673101"],"abstract_inverted_index":{"The":[0,26,53,83],"major":[1],"objective":[2],"of":[3,13,32,64,74,77,93,106,115],"this":[4,23,37],"work":[5],"is":[6,30,45,56,121,132],"to":[7,47,101,123],"evaluate":[8,124],"and":[9,110,128,130],"study":[10],"the":[11,39,50,59,62,65,87,103,107,116,125],"model":[12,27,89],"coronavirus":[14],"illness":[15],"by":[16],"providing":[17],"an":[18,112],"efficient":[19],"numerical":[20,119],"solution":[21],"for":[22],"important":[24],"model.":[25,52],"under":[28],"investigation":[29],"composed":[31],"five":[33],"differential":[34],"equations.":[35,95],"In":[36],"study,":[38],"multidomain":[40],"spectral":[41],"relaxation":[42],"method":[43],"(MSRM)":[44],"used":[46,122],"numerically":[48],"solve":[49],"suggested":[51,108],"proposed":[54,88],"approach":[55],"based":[57],"on":[58],"hypothesis":[60],"that":[61],"domain":[63],"problem":[66],"can":[67,79],"be":[68],"split":[69],"into":[70,90],"a":[71,81,91],"finite":[72],"number":[73],"subintervals,":[75],"each":[76],"which":[78],"have":[80],"solution.":[82],"procedure":[84],"also":[85],"converts":[86],"system":[92],"algebraic":[94],"Some":[96],"theoretical":[97],"studies":[98],"are":[99],"provided":[100],"discuss":[102],"convergence":[104],"analysis":[105],"scheme":[109],"deduce":[111],"upper":[113],"bound":[114],"error.":[117],"A":[118],"simulation":[120],"approach\u2019s":[126],"accuracy":[127],"utility,":[129],"it":[131],"presented":[133],"in":[134],"symmetric":[135],"forms.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}