{"id":"https://openalex.org/W2799993173","doi":"https://doi.org/10.3390/e20050321","title":"Finite Difference Method for Time-Space Fractional Advection\u2013Diffusion Equations with Riesz Derivative","display_name":"Finite Difference Method for Time-Space Fractional Advection\u2013Diffusion Equations with Riesz Derivative","publication_year":2018,"publication_date":"2018-04-26","ids":{"openalex":"https://openalex.org/W2799993173","doi":"https://doi.org/10.3390/e20050321","mag":"2799993173","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265411"},"language":"en","primary_location":{"id":"doi:10.3390/e20050321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050321","pdf_url":"https://www.mdpi.com/1099-4300/20/5/321/pdf?version=1525350035","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/5/321/pdf?version=1525350035","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089893371","display_name":"Sadia Arshad","orcid":"https://orcid.org/0000-0001-9085-5915"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","PK"],"is_corresponding":true,"raw_author_name":"Sadia Arshad","raw_affiliation_strings":["COMSATS Institute of Information Technology, Lahore 54500, Pakistan","The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COMSATS Institute of Information Technology, Lahore 54500, Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030756029","display_name":"Dumitru B\u01celeanu","orcid":"https://orcid.org/0000-0002-0286-7244"},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I4210142834","display_name":"Institute of Space Science - INFLPR Subsidiary","ror":"https://ror.org/054a6wv56","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210142834"]}],"countries":["RO","TR"],"is_corresponding":false,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Cankaya University, Ankara 06530, Turkey","Institute of Space Sciences, Magurele-Bucharest 077125, Romania"],"raw_orcid":"https://orcid.org/0000-0002-0286-7244","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cankaya University, Ankara 06530, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Institute of Space Sciences, Magurele-Bucharest 077125, Romania","institution_ids":["https://openalex.org/I4210142834"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022077594","display_name":"Jianfei Huang","orcid":"https://orcid.org/0000-0002-3793-1277"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianfei Huang","raw_affiliation_strings":["College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111685736","display_name":"M. M. Qurashi","orcid":null},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Maysaa Mohamed Al Qurashi","raw_affiliation_strings":["Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0979-5746","affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111634036","display_name":"Yifa Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yifa Tang","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054215116","display_name":"Y\u00fce Zhao","orcid":"https://orcid.org/0000-0002-9174-0519"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Zhao","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"The State Key Laboratory of Scientific and Engineering Computing (LSEC), The Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC), Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5089893371","https://openalex.org/A5111634036"],"corresponding_institution_ids":["https://openalex.org/I16076960","https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.9682,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.91167795,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"321","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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":0.9980000257492065,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9958999752998352,"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/fractional-calculus","display_name":"Fractional calculus","score":0.7244175672531128},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.6368246078491211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6006036400794983},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5642699003219604},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5532719492912292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4992983341217041},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.47951462864875793},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.4721683859825134},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46191027760505676},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45403051376342773},{"id":"https://openalex.org/keywords/finite-volume-method-for-one-dimensional-steady-state-diffusion","display_name":"Finite volume method for one-dimensional steady state diffusion","score":0.4295791685581207},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2759416699409485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18657582998275757},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10419374704360962},{"id":"https://openalex.org/keywords/innovation-diffusion","display_name":"Innovation diffusion","score":0.08337792754173279},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07536444067955017}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7244175672531128},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.6368246078491211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6006036400794983},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5642699003219604},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5532719492912292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4992983341217041},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.47951462864875793},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.4721683859825134},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46191027760505676},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45403051376342773},{"id":"https://openalex.org/C85405225","wikidata":"https://www.wikidata.org/wiki/Q17013617","display_name":"Finite volume method for one-dimensional steady state diffusion","level":4,"score":0.4295791685581207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2759416699409485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18657582998275757},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10419374704360962},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.08337792754173279},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07536444067955017},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"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":5,"locations":[{"id":"doi:10.3390/e20050321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050321","pdf_url":"https://www.mdpi.com/1099-4300/20/5/321/pdf?version=1525350035","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33265411","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265411","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:2ba3dfa001124fc4a808c8bcc5cdb548","is_oa":true,"landing_page_url":"https://doaj.org/article/2ba3dfa001124fc4a808c8bcc5cdb548","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":"Entropy, Vol 20, Iss 5, p 321 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/5/321/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e20050321","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 20; Issue 5; Pages: 321","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7512840","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512840","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e20050321","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20050321","pdf_url":"https://www.mdpi.com/1099-4300/20/5/321/pdf?version=1525350035","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W204441972","https://openalex.org/W221829734","https://openalex.org/W1539707276","https://openalex.org/W1966513244","https://openalex.org/W1969734198","https://openalex.org/W1978349032","https://openalex.org/W1978929152","https://openalex.org/W1980154613","https://openalex.org/W1982093412","https://openalex.org/W1985496247","https://openalex.org/W1991982189","https://openalex.org/W1994770159","https://openalex.org/W1997347739","https://openalex.org/W2001011967","https://openalex.org/W2008474712","https://openalex.org/W2009063484","https://openalex.org/W2013129097","https://openalex.org/W2020772937","https://openalex.org/W2022486565","https://openalex.org/W2050077166","https://openalex.org/W2059522826","https://openalex.org/W2061878175","https://openalex.org/W2066016807","https://openalex.org/W2083955243","https://openalex.org/W2092942665","https://openalex.org/W2099111135","https://openalex.org/W2107162131","https://openalex.org/W2111271983","https://openalex.org/W2118160506","https://openalex.org/W2140620666","https://openalex.org/W2143130504","https://openalex.org/W2144260588","https://openalex.org/W2161701360","https://openalex.org/W2170885741","https://openalex.org/W2279429433","https://openalex.org/W2510317682","https://openalex.org/W2513064071","https://openalex.org/W2611468712","https://openalex.org/W2641517145","https://openalex.org/W2690732668","https://openalex.org/W2732661672","https://openalex.org/W2749518762","https://openalex.org/W2776784679","https://openalex.org/W2799993173","https://openalex.org/W2908497147","https://openalex.org/W3106522901","https://openalex.org/W4298959008","https://openalex.org/W6608239629","https://openalex.org/W6632296632"],"related_works":["https://openalex.org/W2528667048","https://openalex.org/W2099172367","https://openalex.org/W2954522738","https://openalex.org/W2501432554","https://openalex.org/W2114549045","https://openalex.org/W4283652870","https://openalex.org/W2114010261","https://openalex.org/W2154880380","https://openalex.org/W2234041809","https://openalex.org/W4253925511"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"a":[3],"numerical":[4],"scheme":[5,93],"is":[6,37,76,94],"formulated":[7],"and":[8,21,29,44,57,85,105],"analysed":[9],"to":[10,112],"solve":[11],"the":[12,18,22,40,50,53,58,64,74,79,83,98,114],"time-space":[13],"fractional":[14,42,54,65],"advection-diffusion":[15],"equation,":[16,60],"where":[17],"Riesz":[19,34],"derivative":[20,24,36],"Caputo":[23],"are":[25,88,109],"considered":[26],"in":[27,103],"spatial":[28],"temporal":[30],"directions,":[31],"respectively.":[32],"The":[33,91],"space":[35,104],"approximated":[38,77],"by":[39,78],"second-order":[41],"weighted":[43],"shifted":[45],"Gr\u00fcnwald-Letnikov":[46],"formula.":[47,81],"Based":[48],"on":[49],"equivalence":[51],"between":[52],"differential":[55,66],"equation":[56,67],"integral":[59,71,75],"we":[61],"have":[62],"transformed":[63],"into":[68],"an":[69],"equivalent":[70],"equation.":[72],"Then,":[73],"trapezoidal":[80],"Further,":[82],"stability":[84],"convergence":[86],"analysis":[87],"discussed":[89],"rigorously.":[90],"resulting":[92],"formally":[95],"proved":[96],"with":[97],"second":[99],"order":[100],"accuracy":[101],"both":[102],"time.":[106],"Numerical":[107],"experiments":[108],"also":[110],"presented":[111],"verify":[113],"theoretical":[115],"analysis.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}