{"id":"https://openalex.org/W2057769307","doi":"https://doi.org/10.1137/090771715","title":"Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation","display_name":"Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2057769307","doi":"https://doi.org/10.1137/090771715","mag":"2057769307"},"language":"en","primary_location":{"id":"doi:10.1137/090771715","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771715","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5103161863","display_name":"Chang\u2010Ming Chen","orcid":"https://orcid.org/0000-0002-8289-8277"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang-Ming Chen","raw_affiliation_strings":["cmchen@xmu.edu.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"cmchen@xmu.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090768752","display_name":"F. Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Liu","raw_affiliation_strings":["f.liu@qut.edu.au and v.anh@qut.edu.au and i.turner@qut.edu.au#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"f.liu@qut.edu.au and v.anh@qut.edu.au and i.turner@qut.edu.au#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061268303","display_name":"Vo Anh","orcid":"https://orcid.org/0000-0003-2463-2099"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Anh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007130769","display_name":"Ian Turner","orcid":"https://orcid.org/0000-0003-2794-3968"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Turner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6387,"has_fulltext":false,"cited_by_count":233,"citation_normalized_percentile":{"value":0.97880394,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"32","issue":"4","first_page":"1740","last_page":"1760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T10514","display_name":"Numerical methods in engineering","score":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.7714117765426636},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6314116716384888},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.601499617099762},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5974954962730408},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.583869457244873},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5238649845123291},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.52137690782547},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.48624885082244873},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.4331167936325073},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4200561046600342},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.38838106393814087},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.37134987115859985},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.286876380443573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1365729570388794}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7714117765426636},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6314116716384888},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.601499617099762},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5974954962730408},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.583869457244873},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5238649845123291},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.52137690782547},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.48624885082244873},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.4331167936325073},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4200561046600342},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.38838106393814087},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.37134987115859985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.286876380443573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1365729570388794},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090771715","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090771715","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:researchbank.swinburne.edu.au:d5d4a964-b7d3-4c3d-9d09-c4d493c4d70e/1","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.3/452818","pdf_url":null,"source":{"id":"https://openalex.org/S4306401157","display_name":"Swinburne Research Bank (Swinburne University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I57093077","host_organization_name":"Swinburne University of Technology","host_organization_lineage":["https://openalex.org/I57093077"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, Vol. 32, no. 4 (Jan 2010), pp. 1740-1760","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W110340196","https://openalex.org/W1546248182","https://openalex.org/W1571391776","https://openalex.org/W1963563982","https://openalex.org/W1970403427","https://openalex.org/W1974234252","https://openalex.org/W1977696410","https://openalex.org/W1979294180","https://openalex.org/W1980154613","https://openalex.org/W1981690041","https://openalex.org/W1985968362","https://openalex.org/W1988499281","https://openalex.org/W1997347739","https://openalex.org/W1997700622","https://openalex.org/W2001031344","https://openalex.org/W2005329489","https://openalex.org/W2012163408","https://openalex.org/W2016124038","https://openalex.org/W2017663693","https://openalex.org/W2021735811","https://openalex.org/W2022352949","https://openalex.org/W2024990358","https://openalex.org/W2027205768","https://openalex.org/W2041827099","https://openalex.org/W2045514685","https://openalex.org/W2050981193","https://openalex.org/W2056829543","https://openalex.org/W2064641940","https://openalex.org/W2066053624","https://openalex.org/W2081196614","https://openalex.org/W2093108432","https://openalex.org/W2098263458","https://openalex.org/W2105723279","https://openalex.org/W2109328281","https://openalex.org/W2111271983","https://openalex.org/W2116024271","https://openalex.org/W2118843959","https://openalex.org/W2119671522","https://openalex.org/W2125366357","https://openalex.org/W2137696066","https://openalex.org/W2154277570","https://openalex.org/W2165076033","https://openalex.org/W2732661672"],"related_works":["https://openalex.org/W1984031140","https://openalex.org/W2034082304","https://openalex.org/W81470468","https://openalex.org/W1964268922","https://openalex.org/W1968864649","https://openalex.org/W2066908446","https://openalex.org/W2102789413","https://openalex.org/W2553664144","https://openalex.org/W2913782054","https://openalex.org/W2056289616"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"a":[5],"variable-order":[6],"anomalous":[7],"subdiffusion":[8],"equation.":[9],"A":[10],"numerical":[11,35,47,63],"scheme":[12,36,48],"with":[13,49],"first":[14],"order":[15,20,51,56],"temporal":[16,52],"accuracy":[17,22,53,58],"and":[18,31,54,67],"fourth":[19,55],"spatial":[21,57],"for":[23],"the":[24,34,40,68,71],"equation":[25],"is":[26,59],"proposed.":[27,61],"The":[28],"convergence,":[29],"stability,":[30],"solvability":[32],"of":[33,42,73],"are":[37,65],"discussed":[38],"via":[39],"technique":[41],"Fourier":[43],"analysis.":[44,75],"Another":[45],"improved":[46],"second":[50],"also":[60],"Some":[62],"examples":[64],"given,":[66],"results":[69],"demonstrate":[70],"effectiveness":[72],"theoretical":[74]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":23},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}