{"id":"https://openalex.org/W3087635831","doi":"https://doi.org/10.3390/sym12091560","title":"Exact Solutions and Continuous Numerical Approximations of Coupled Systems of Diffusion Equations with Delay","display_name":"Exact Solutions and Continuous Numerical Approximations of Coupled Systems of Diffusion Equations with Delay","publication_year":2020,"publication_date":"2020-09-21","ids":{"openalex":"https://openalex.org/W3087635831","doi":"https://doi.org/10.3390/sym12091560","mag":"3087635831"},"language":"en","primary_location":{"id":"doi:10.3390/sym12091560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091560","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1560/pdf?version=1600829465","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/2073-8994/12/9/1560/pdf?version=1600829465","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062481296","display_name":"Elia Reyes","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Elia Reyes","raw_affiliation_strings":["Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014338702","display_name":"Mar\u00eda \u00c1ngeles Castro","orcid":"https://orcid.org/0000-0003-4331-4619"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. \u00c1ngeles Castro","raw_affiliation_strings":["Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4331-4619","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030158061","display_name":"Antonio Sirvent","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonio Sirvent","raw_affiliation_strings":["Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019831447","display_name":"Francisco Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-0753-7826"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco Rodr\u00edguez","raw_affiliation_strings":["Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain","Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Apdo. 99, 03080 Alicante, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0753-7826","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Alicante, Apdo. 99, 03080 Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]},{"raw_affiliation_string":"Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Apdo. 99, 03080 Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019831447"],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8904,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72360535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"9","first_page":"1560","last_page":"1560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9983999729156494,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.6481069326400757},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6297496557235718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.585878849029541},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5584231615066528},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4990823268890381},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4968455135822296},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.476458340883255},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.43451541662216187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35862985253334045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23123478889465332},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11289283633232117}],"concepts":[{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.6481069326400757},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6297496557235718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.585878849029541},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5584231615066528},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4990823268890381},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4968455135822296},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.476458340883255},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.43451541662216187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35862985253334045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23123478889465332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11289283633232117},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12091560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091560","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1560/pdf?version=1600829465","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:dnet:ruarepositor::b5508ed0ce34d749a8e4b1b9ae596c80","is_oa":true,"landing_page_url":"http://hdl.handle.net/10045/109402","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:a8b5df0bc43141d1b43d8fd4103f6f29","is_oa":true,"landing_page_url":"https://doaj.org/article/a8b5df0bc43141d1b43d8fd4103f6f29","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 9, p 1560 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/9/1560/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12091560","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/sym12091560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091560","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1560/pdf?version=1600829465","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":[{"id":"https://openalex.org/G743339841","display_name":null,"funder_award_id":"CGL2017-89804-R","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3087635831.pdf","grobid_xml":"https://content.openalex.org/works/W3087635831.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W125153771","https://openalex.org/W565987384","https://openalex.org/W752886854","https://openalex.org/W1494118823","https://openalex.org/W1580071822","https://openalex.org/W1586658033","https://openalex.org/W1605753492","https://openalex.org/W1984113283","https://openalex.org/W2010868003","https://openalex.org/W2016230799","https://openalex.org/W2036672063","https://openalex.org/W2041333630","https://openalex.org/W2045417540","https://openalex.org/W2047017331","https://openalex.org/W2074824556","https://openalex.org/W2087037621","https://openalex.org/W2087273716","https://openalex.org/W2871112201","https://openalex.org/W2934148492","https://openalex.org/W2951952122","https://openalex.org/W2986160045","https://openalex.org/W3080425940","https://openalex.org/W3196570301","https://openalex.org/W4211103870","https://openalex.org/W4229842459","https://openalex.org/W6801188783"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W4229058035","https://openalex.org/W1919101720","https://openalex.org/W3125672081","https://openalex.org/W2006389905","https://openalex.org/W4297797135","https://openalex.org/W2904666330"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,45],"obtain":[4,46],"exact":[5,47],"solutions":[6,50,58],"and":[7,29],"continuous":[8],"numerical":[9],"approximations":[10],"for":[11,35],"mixed":[12],"problems":[13],"of":[14,17,25,27,38,73,75],"coupled":[15],"systems":[16],"diffusion":[18],"equations":[19],"with":[20,59,80],"delay.":[21],"Using":[22],"the":[23,36,39,71],"method":[24,72],"separation":[26,74],"variables,":[28],"based":[30],"on":[31],"an":[32],"explicit":[33],"expression":[34],"solution":[37],"separated":[40],"vector":[41],"initial-value":[42],"delay":[43],"problem,":[44],"infinite":[48],"series":[49],"that":[51],"can":[52],"be":[53],"truncated":[54],"to":[55],"provide":[56],"analytical\u2013numerical":[57],"prescribed":[60],"accuracy":[61],"in":[62,68],"bounded":[63],"domains.":[64],"Although":[65],"usually":[66],"implicit":[67],"particular":[69],"applications,":[70],"variables":[76],"is":[77],"deeply":[78],"correlated":[79],"symmetry":[81],"ideas.":[82]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
