{"id":"https://openalex.org/W4402541321","doi":"https://doi.org/10.3934/nhm.2024041","title":"A modified domain decomposition spectral collocation method for parabolic partial differential equations","display_name":"A modified domain decomposition spectral collocation method for parabolic partial differential equations","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4402541321","doi":"https://doi.org/10.3934/nhm.2024041"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2024041","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2024041","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://dx.doi.org/10.3934/nhm.2024041","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007632375","display_name":"Wei\u2010Hua Luo","orcid":"https://orcid.org/0000-0003-1343-6973"},"institutions":[{"id":"https://openalex.org/I196038209","display_name":"Hunan University of Arts and Science","ror":"https://ror.org/01ggnn306","country_code":"CN","type":"education","lineage":["https://openalex.org/I196038209"]},{"id":"https://openalex.org/I4210117337","display_name":"Neijiang Normal University","ror":"https://ror.org/02bc8tz70","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei-Hua Luo","raw_affiliation_strings":["Laboratory of Numerical Simulation of Sichuan Provincial Universities, Neijiang Normal University, Neijiang, Sichuan, 641000, P.R. China","School of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Numerical Simulation of Sichuan Provincial Universities, Neijiang Normal University, Neijiang, Sichuan, 641000, P.R. China","institution_ids":["https://openalex.org/I4210117337"]},{"raw_affiliation_string":"School of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P.R. China","institution_ids":["https://openalex.org/I196038209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101601320","display_name":"Liang Yin","orcid":"https://orcid.org/0000-0001-6399-1399"},"institutions":[{"id":"https://openalex.org/I196038209","display_name":"Hunan University of Arts and Science","ror":"https://ror.org/01ggnn306","country_code":"CN","type":"education","lineage":["https://openalex.org/I196038209"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Yin","raw_affiliation_strings":["College of Mechanical Engineering, Hunan University of Arts and Science, Changde, Hunan, 415000, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mechanical Engineering, Hunan University of Arts and Science, Changde, Hunan, 415000, P.R. China","institution_ids":["https://openalex.org/I196038209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100419613","display_name":"Jun Guo","orcid":"https://orcid.org/0000-0001-9867-2689"},"institutions":[{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Guo","raw_affiliation_strings":["College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, 610225, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, 610225, P.R. China","institution_ids":["https://openalex.org/I24201400"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15660412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"3","first_page":"923","last_page":"939"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6659184694290161},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.650814950466156},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6380398869514465},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.6055086255073547},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5723596215248108},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5537914037704468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5499765276908875},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5310842394828796},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.48765552043914795},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.47079697251319885},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.46134573221206665},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.44115614891052246},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3891529142856598},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3664225935935974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2820017337799072},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.16282051801681519},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15643873810768127},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11071133613586426},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.104501873254776},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10124191641807556}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6659184694290161},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.650814950466156},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6380398869514465},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.6055086255073547},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5723596215248108},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5537914037704468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5499765276908875},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5310842394828796},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.48765552043914795},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.47079697251319885},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.46134573221206665},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.44115614891052246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3891529142856598},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3664225935935974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2820017337799072},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.16282051801681519},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15643873810768127},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11071133613586426},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.104501873254776},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10124191641807556},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0},{"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2024041","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2024041","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7a9ef9ce1a29457e812acfdcf254ec2e","is_oa":false,"landing_page_url":"https://doaj.org/article/7a9ef9ce1a29457e812acfdcf254ec2e","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":"Networks and Heterogeneous Media, Vol 19, Iss 3, Pp 923-939 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2024041","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2024041","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1966584387","https://openalex.org/W1971462346","https://openalex.org/W1981068439","https://openalex.org/W1991850042","https://openalex.org/W2038962495","https://openalex.org/W2093895095","https://openalex.org/W2172187730","https://openalex.org/W2522963784","https://openalex.org/W2561980341","https://openalex.org/W2571181132","https://openalex.org/W2582027428","https://openalex.org/W2760796820","https://openalex.org/W2955253682","https://openalex.org/W2964230707","https://openalex.org/W2979568270","https://openalex.org/W3026183760","https://openalex.org/W3035895011","https://openalex.org/W3086819502","https://openalex.org/W3092325308","https://openalex.org/W3128593186","https://openalex.org/W4295990936","https://openalex.org/W4388051474"],"related_works":["https://openalex.org/W2158514508","https://openalex.org/W2806218632","https://openalex.org/W3033023825","https://openalex.org/W3096143543","https://openalex.org/W2566202876","https://openalex.org/W2990545979","https://openalex.org/W2123838659","https://openalex.org/W2011929594","https://openalex.org/W1848947320","https://openalex.org/W1590043565"],"abstract_inverted_index":{"<p>In":[0],"this":[1],"paper,":[2],"utilizing":[3],"Legendre":[4],"polynomials":[5],"as":[6],"the":[7,31,43,48,57,60,64,67],"basis":[8],"functions":[9],"in":[10],"both":[11],"space":[12],"and":[13,63],"time,":[14],"we":[15],"present":[16],"a":[17,36],"modified":[18],"domain":[19],"decomposition":[20],"spectral":[21],"method":[22,62],"for":[23],"2-dimensional":[24],"parabolic":[25],"partial":[26],"differential":[27],"equations.":[28],"For":[29],"solving":[30],"obtained":[32,44],"linear/nonlinear":[33],"algebraic":[34],"equations,":[35],"dimension":[37],"expanding":[38],"preconditioner":[39],"is":[40],"applied":[41],"employing":[42],"saddle":[45],"construction":[46],"of":[47,59,66],"coefficient":[49],"matrix.":[50],"Numerical":[51],"examples":[52],"are":[53],"given":[54],"to":[55],"show":[56],"performance":[58],"presented":[61],"efficiency":[65],"preconditioner.</p>":[68]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}