{"id":"https://openalex.org/W4407684399","doi":"https://doi.org/10.1007/s10700-025-09439-z","title":"Numerical solution of uncertain partial differential equations and its applications","display_name":"Numerical solution of uncertain partial differential equations and its applications","publication_year":2025,"publication_date":"2025-02-18","ids":{"openalex":"https://openalex.org/W4407684399","doi":"https://doi.org/10.1007/s10700-025-09439-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10700-025-09439-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-025-09439-z","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","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/A5016078460","display_name":"Lu Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210100953","display_name":"Xi'an University of Finance and Economics","ror":"https://ror.org/01b9y2p27","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210100953"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Yang","raw_affiliation_strings":["Department of Statistics, Xi\u2019an University of Finance and Economics, Xi\u2019an, 710100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Xi\u2019an University of Finance and Economics, Xi\u2019an, 710100, China","institution_ids":["https://openalex.org/I4210100953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034753318","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0003-0780-8267"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yang Liu","raw_affiliation_strings":["School of Economics and Management, Beihang University, Beijing, 100191, China"],"raw_orcid":"https://orcid.org/0000-0003-0780-8267","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034753318"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":9.9565,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.98461305,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"69","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9524999856948853,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9521999955177307,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5583420395851135},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5269580483436584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5064913034439087},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.49907708168029785},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.41998499631881714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3780378997325897},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36914098262786865},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.35993319749832153},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30935779213905334},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.22989293932914734},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.17292249202728271}],"concepts":[{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5583420395851135},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5269580483436584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5064913034439087},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.49907708168029785},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.41998499631881714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3780378997325897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36914098262786865},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35993319749832153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30935779213905334},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.22989293932914734},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.17292249202728271}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10700-025-09439-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-025-09439-z","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:fuzodm:v:24:y:2025:i:1:d:10.1007_s10700-025-09439-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10700-025-09439-z","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7409651771","display_name":null,"funder_award_id":"2024M764105","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1602939453","https://openalex.org/W2152380123","https://openalex.org/W2164919501","https://openalex.org/W2523879549","https://openalex.org/W2898611589","https://openalex.org/W3089122089","https://openalex.org/W3197622967","https://openalex.org/W3207623001","https://openalex.org/W4206830167","https://openalex.org/W4220822722","https://openalex.org/W4281775731","https://openalex.org/W4293708200","https://openalex.org/W4306693045","https://openalex.org/W4313396145","https://openalex.org/W4362515176","https://openalex.org/W4385458884","https://openalex.org/W4386119809","https://openalex.org/W4387779022","https://openalex.org/W4388811102","https://openalex.org/W4388830389","https://openalex.org/W4402718019","https://openalex.org/W6678868654","https://openalex.org/W6682597882"],"related_works":["https://openalex.org/W3020098708","https://openalex.org/W2006263304","https://openalex.org/W3147000368","https://openalex.org/W2357676173","https://openalex.org/W2058110277","https://openalex.org/W3141884580","https://openalex.org/W4320000718","https://openalex.org/W185970870","https://openalex.org/W3196497253","https://openalex.org/W3092397470"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}