{"id":"https://openalex.org/W2009239825","doi":"https://doi.org/10.1090/s0025-5718-2011-02447-6","title":"Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation","display_name":"Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation","publication_year":2011,"publication_date":"2011-06-09","ids":{"openalex":"https://openalex.org/W2009239825","doi":"https://doi.org/10.1090/s0025-5718-2011-02447-6","mag":"2009239825"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02447-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02447-6","pdf_url":"https://www.ams.org/mcom/2012-81-277/S0025-5718-2011-02447-6/S0025-5718-2011-02447-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2012-81-277/S0025-5718-2011-02447-6/S0025-5718-2011-02447-6.pdf","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":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chang-Ming Chen","raw_affiliation_strings":["School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041746046","display_name":"F. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"F. Liu","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061268303","display_name":"Vo Anh","orcid":"https://orcid.org/0000-0003-2463-2099"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"V. Anh","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007130769","display_name":"Ian Turner","orcid":"https://orcid.org/0000-0003-2794-3968"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"I. Turner","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia","institution_ids":["https://openalex.org/I160993911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.5718,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.97349823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"81","issue":"277","first_page":"345","last_page":"366"},"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8483197689056396},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6038791537284851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5326988697052002},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5074791312217712},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33504098653793335}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8483197689056396},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6038791537284851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5326988697052002},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5074791312217712},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33504098653793335},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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:10.1090/s0025-5718-2011-02447-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02447-6","pdf_url":"https://www.ams.org/mcom/2012-81-277/S0025-5718-2011-02447-6/S0025-5718-2011-02447-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:researchbank.swinburne.edu.au:c059e5ad-e632-490d-b3fb-6063582dc99e/1","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.3/446198","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":"Mathematics of Computation, Vol. 81, no. 277 (Jan 2012), pp. 345-366","raw_type":null}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02447-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02447-6","pdf_url":"https://www.ams.org/mcom/2012-81-277/S0025-5718-2011-02447-6/S0025-5718-2011-02447-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.49000000953674316,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G5071633448","display_name":"Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics","funder_award_id":"DP0559807","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G8030262125","display_name":null,"funder_award_id":"10271098","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8232661776","display_name":"A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media","funder_award_id":"DP0986766","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2009239825.pdf","grobid_xml":"https://content.openalex.org/works/W2009239825.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W1546248182","https://openalex.org/W1562918138","https://openalex.org/W1569035865","https://openalex.org/W1571391776","https://openalex.org/W1977696410","https://openalex.org/W1979294180","https://openalex.org/W1985968362","https://openalex.org/W1988499281","https://openalex.org/W1989307095","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/W2024010633","https://openalex.org/W2033471049","https://openalex.org/W2038780460","https://openalex.org/W2041827099","https://openalex.org/W2050981193","https://openalex.org/W2052671664","https://openalex.org/W2055962432","https://openalex.org/W2056829543","https://openalex.org/W2064641940","https://openalex.org/W2081196614","https://openalex.org/W2097711273","https://openalex.org/W2098263458","https://openalex.org/W2113148983","https://openalex.org/W2116024271","https://openalex.org/W2119671522","https://openalex.org/W2127684492","https://openalex.org/W2142758723","https://openalex.org/W2165076033","https://openalex.org/W2732661672","https://openalex.org/W2787959293","https://openalex.org/W4289798260","https://openalex.org/W4289813016","https://openalex.org/W6600157417","https://openalex.org/W6600280466","https://openalex.org/W6600478496","https://openalex.org/W6601328799","https://openalex.org/W6601439933","https://openalex.org/W6602602802","https://openalex.org/W6604009900","https://openalex.org/W6605040138","https://openalex.org/W6605894717","https://openalex.org/W6607380909","https://openalex.org/W6634186679","https://openalex.org/W6640309798","https://openalex.org/W6677277677","https://openalex.org/W6758891008"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Anomalous":[0],"subdiffusion":[1,19],"equations":[2],"have":[3],"in":[4],"recent":[5],"years":[6],"received":[7],"much":[8],"attention.":[9],"In":[10],"this":[11],"paper,":[12],"we":[13],"consider":[14],"a":[15],"two-dimensional":[16],"variable-order":[17],"anomalous":[18],"equation.":[20,34],"Two":[21],"numerical":[22,57],"methods":[23],"(the":[24],"implicit":[25],"and":[26,38],"explicit":[27],"methods)":[28],"are":[29,40],"developed":[30],"to":[31],"solve":[32],"the":[33,43,47],"Their":[35],"stability,":[36],"convergence":[37],"solvability":[39],"investigated":[41],"by":[42,55],"Fourier":[44],"method.":[45],"Moreover,":[46],"effectiveness":[48],"of":[49],"our":[50],"theoretical":[51],"analysis":[52],"is":[53],"demonstrated":[54],"some":[56],"examples.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}