{"id":"https://openalex.org/W4283762640","doi":"https://doi.org/10.1155/2022/8998193","title":"Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation","display_name":"Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283762640","doi":"https://doi.org/10.1155/2022/8998193"},"language":"en","primary_location":{"id":"doi:10.1155/2022/8998193","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8998193","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/8998193.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2022/8998193.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016171406","display_name":"Jin Li","orcid":"https://orcid.org/0000-0001-6887-7720"},"institutions":[{"id":"https://openalex.org/I44445938","display_name":"Shandong Jianzhu University","ror":"https://ror.org/01gbfax37","country_code":"CN","type":"education","lineage":["https://openalex.org/I44445938"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jin Li","raw_affiliation_strings":["School of Science, Shandong Jianzhu University, Jinan 250101, China"],"raw_orcid":"https://orcid.org/0000-0001-6887-7720","affiliations":[{"raw_affiliation_string":"School of Science, Shandong Jianzhu University, Jinan 250101, China","institution_ids":["https://openalex.org/I44445938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016171406"],"corresponding_institution_ids":["https://openalex.org/I44445938"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06071806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2022","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9973000288009644,"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":0.9973000288009644,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9973000288009644,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.7606509923934937},{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.7312250137329102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7089256644248962},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5843622088432312},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5838175415992737},{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.5836233496665955},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.52793949842453},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5276248455047607},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5166340470314026},{"id":"https://openalex.org/keywords/relativistic-heat-conduction","display_name":"Relativistic heat conduction","score":0.45005887746810913},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3559410274028778},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.2170267105102539},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1666555106639862},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10473430156707764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09737947583198547},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09368690848350525},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08182153105735779},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.06509542465209961},{"id":"https://openalex.org/keywords/heat-flux","display_name":"Heat flux","score":0.046176642179489136}],"concepts":[{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7606509923934937},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.7312250137329102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7089256644248962},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5843622088432312},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5838175415992737},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.5836233496665955},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.52793949842453},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5276248455047607},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5166340470314026},{"id":"https://openalex.org/C43818450","wikidata":"https://www.wikidata.org/wiki/Q7310828","display_name":"Relativistic heat conduction","level":4,"score":0.45005887746810913},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3559410274028778},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.2170267105102539},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1666555106639862},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10473430156707764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09737947583198547},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09368690848350525},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08182153105735779},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.06509542465209961},{"id":"https://openalex.org/C159188206","wikidata":"https://www.wikidata.org/wiki/Q1478382","display_name":"Heat flux","level":3,"score":0.046176642179489136},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2022/8998193","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8998193","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/8998193.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnljam:8998193","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/jam/2022/8998193.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:bd9b352595df4564beffe0f7c5ff6076","is_oa":true,"landing_page_url":"https://doaj.org/article/bd9b352595df4564beffe0f7c5ff6076","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":"Journal of Applied Mathematics, Vol 2022 (2022)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2022/8998193","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/8998193","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2022/8998193","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/8998193","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/8998193.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2209847612","display_name":null,"funder_award_id":"Grant No. A2019209533","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"},{"id":"https://openalex.org/G5061914213","display_name":null,"funder_award_id":"A2019209533","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283762640.pdf","grobid_xml":"https://content.openalex.org/works/W4283762640.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1597222877","https://openalex.org/W1991334951","https://openalex.org/W1991838779","https://openalex.org/W1992153626","https://openalex.org/W2000118209","https://openalex.org/W2011851385","https://openalex.org/W2047035051","https://openalex.org/W2049897010","https://openalex.org/W2091456785","https://openalex.org/W2171388031","https://openalex.org/W2517096890","https://openalex.org/W2611013241","https://openalex.org/W2771012542","https://openalex.org/W2808915437","https://openalex.org/W3007176864","https://openalex.org/W3081652472","https://openalex.org/W3083000207","https://openalex.org/W3101059446","https://openalex.org/W3129852679","https://openalex.org/W3166423341","https://openalex.org/W4231414267","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2131278000","https://openalex.org/W2889856026","https://openalex.org/W2009058751","https://openalex.org/W2478942264","https://openalex.org/W1989122168"],"abstract_inverted_index":{"Nonlinear":[0],"heat":[1,26,37],"equation":[2,28,39],"solved":[3],"by":[4],"the":[5,24],"barycentric":[6],"rational":[7],"collocation":[8],"method":[9,15,19],"(BRCM)":[10],"is":[11,40],"presented.":[12],"Direct":[13],"linearization":[14,18],"and":[16],"Newton":[17],"are":[20,46],"presented":[21],"to":[22,48],"transform":[23],"nonlinear":[25,36],"conduction":[27,38],"into":[29],"linear":[30],"equations.":[31],"The":[32],"matrix":[33],"form":[34],"of":[35],"also":[41],"obtained.":[42],"Several":[43],"numerical":[44],"examples":[45],"provided":[47],"valid":[49],"our":[50],"schemes.":[51]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}