{"id":"https://openalex.org/W3012598748","doi":"https://doi.org/10.3390/sym12030485","title":"Finite Difference Approximation Method for a Space Fractional Convection\u2013Diffusion Equation with Variable Coefficients","display_name":"Finite Difference Approximation Method for a Space Fractional Convection\u2013Diffusion Equation with Variable Coefficients","publication_year":2020,"publication_date":"2020-03-23","ids":{"openalex":"https://openalex.org/W3012598748","doi":"https://doi.org/10.3390/sym12030485","mag":"3012598748"},"language":"en","primary_location":{"id":"doi:10.3390/sym12030485","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12030485","pdf_url":"https://www.mdpi.com/2073-8994/12/3/485/pdf?version=1584960134","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/3/485/pdf?version=1584960134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063605980","display_name":"Eyaya Fekadie Anley","orcid":"https://orcid.org/0000-0002-3723-0059"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I42869670","display_name":"Arba Minch University","ror":"https://ror.org/00ssp9h11","country_code":"ET","type":"education","lineage":["https://openalex.org/I42869670"]}],"countries":["CN","ET"],"is_corresponding":false,"raw_author_name":"Eyaya Fekadie Anley","raw_affiliation_strings":["College of Natural and Computational Science, Department of Mathematics, Arba-Minch University, Arba-Minch 21, Ethiopia","School of Mathematics and Statistics, Central South University, Changsha 410083, China"],"raw_orcid":"https://orcid.org/0000-0002-3723-0059","affiliations":[{"raw_affiliation_string":"College of Natural and Computational Science, Department of Mathematics, Arba-Minch University, Arba-Minch 21, Ethiopia","institution_ids":["https://openalex.org/I42869670"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005175256","display_name":"Zhoushun Zheng","orcid":"https://orcid.org/0000-0002-8792-6310"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhoushun Zheng","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha 410083, China"],"raw_orcid":"https://orcid.org/0000-0002-8792-6310","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005175256"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.7588,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.78254111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"485","last_page":"485"},"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":0.9990000128746033,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.7411898970603943},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.6919038891792297},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5802035927772522},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5449657440185547},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5308146476745605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5236009359359741},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.5231003761291504},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5176966190338135},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5134223699569702},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4858946204185486},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.47364962100982666},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.45902496576309204},{"id":"https://openalex.org/keywords/numerical-solution-of-the-convection\u2013diffusion-equation","display_name":"Numerical solution of the convection\u2013diffusion equation","score":0.4301929473876953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40755146741867065},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21268567442893982},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10935398936271667},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08702099323272705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7411898970603943},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.6919038891792297},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5802035927772522},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5449657440185547},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5308146476745605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5236009359359741},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.5231003761291504},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5176966190338135},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5134223699569702},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4858946204185486},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.47364962100982666},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45902496576309204},{"id":"https://openalex.org/C101303905","wikidata":"https://www.wikidata.org/wiki/Q17104838","display_name":"Numerical solution of the convection\u2013diffusion equation","level":4,"score":0.4301929473876953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40755146741867065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21268567442893982},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10935398936271667},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08702099323272705},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym12030485","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12030485","pdf_url":"https://www.mdpi.com/2073-8994/12/3/485/pdf?version=1584960134","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:68d921eed1134982ac4c33cc08d375e8","is_oa":true,"landing_page_url":"https://doaj.org/article/68d921eed1134982ac4c33cc08d375e8","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":"Symmetry, Vol 12, Iss 3, p 485 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym12030485","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12030485","pdf_url":"https://www.mdpi.com/2073-8994/12/3/485/pdf?version=1584960134","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3080998458","display_name":null,"funder_award_id":"2017YFB0305601 and 2017YFB0701700","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012598748.pdf","grobid_xml":"https://content.openalex.org/works/W3012598748.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W902939226","https://openalex.org/W1418158239","https://openalex.org/W1557415511","https://openalex.org/W1867557224","https://openalex.org/W1981956153","https://openalex.org/W1995066738","https://openalex.org/W2001011967","https://openalex.org/W2006359060","https://openalex.org/W2014765146","https://openalex.org/W2025672056","https://openalex.org/W2030139351","https://openalex.org/W2034221093","https://openalex.org/W2042250814","https://openalex.org/W2049030310","https://openalex.org/W2052728710","https://openalex.org/W2054899953","https://openalex.org/W2056061743","https://openalex.org/W2066693071","https://openalex.org/W2070754886","https://openalex.org/W2080928512","https://openalex.org/W2088426359","https://openalex.org/W2099111135","https://openalex.org/W2105723279","https://openalex.org/W2107162131","https://openalex.org/W2123047596","https://openalex.org/W2124303144","https://openalex.org/W2141494273","https://openalex.org/W2188190988","https://openalex.org/W2259227674","https://openalex.org/W2271134218","https://openalex.org/W2290964926","https://openalex.org/W2466528548","https://openalex.org/W2467982773","https://openalex.org/W2592662912","https://openalex.org/W2757164042","https://openalex.org/W2767741824","https://openalex.org/W2963596250","https://openalex.org/W2964228534","https://openalex.org/W4244063180","https://openalex.org/W4247953052","https://openalex.org/W6663427287","https://openalex.org/W6687025702","https://openalex.org/W6694030294"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2171402820","https://openalex.org/W4251142058","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W3115006473","https://openalex.org/W3005239502"],"abstract_inverted_index":{"Space":[0],"non-integer":[1],"order":[2,10,71,99],"convection\u2013diffusion":[3,11,31],"descriptions":[4],"are":[5,87],"generalized":[6],"form":[7],"of":[8,69,93,100],"integer":[9],"problems":[12],"expressing":[13],"super":[14],"diffusive":[15],"and":[16,44,65,76,97],"convective":[17],"transport":[18],"processes.":[19],"In":[20],"this":[21],"article,":[22],"we":[23],"propose":[24],"finite":[25],"difference":[26,52,60],"approximation":[27],"for":[28],"space":[29,34],"fractional":[30],"model":[32],"having":[33],"variable":[35],"coefficients":[36],"on":[37,55],"the":[38,50,56,82,91],"given":[39],"bounded":[40],"domain":[41],"over":[42],"time":[43],"space.":[45],"It":[46],"is":[47,62,67],"shown":[48],"that":[49],"Crank\u2013Nicolson":[51],"scheme":[53],"based":[54],"right":[57],"shifted":[58],"Gr\u00fcnwald\u2013Letnikov":[59],"formula":[61],"unconditionally":[63],"stable":[64],"it":[66],"also":[68],"second":[70],"consistency":[72],"both":[73],"in":[74],"temporal":[75],"spatial":[77],"terms":[78],"with":[79],"extrapolation":[80],"to":[81,89],"limit":[83],"approach.":[84],"Numerical":[85],"experiments":[86],"tested":[88],"verify":[90],"efficiency":[92],"our":[94],"theoretical":[95],"analysis":[96],"confirm":[98],"convergence.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}