{"id":"https://openalex.org/W2754675081","doi":"https://doi.org/10.1080/00207160.2017.1378810","title":"The finite difference method for Caputo-type parabolic equation with fractional Laplacian: more than one space dimension","display_name":"The finite difference method for Caputo-type parabolic equation with fractional Laplacian: more than one space dimension","publication_year":2017,"publication_date":"2017-09-12","ids":{"openalex":"https://openalex.org/W2754675081","doi":"https://doi.org/10.1080/00207160.2017.1378810","mag":"2754675081"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1378810","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1378810","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5061778327","display_name":"Ye Hu","orcid":"https://orcid.org/0000-0001-9664-9426"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I4210148119","display_name":"Luliang University","ror":"https://ror.org/05495v729","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148119"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Hu","raw_affiliation_strings":["Department of Mathematics, Lvliang University, Lishi, China","Department of Mathematics, Shanghai University, Shanghai China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lvliang University, Lishi, China","institution_ids":["https://openalex.org/I4210148119"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088246745","display_name":"Changpin Li","orcid":"https://orcid.org/0000-0003-2012-2788"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Changpin Li","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074042177","display_name":"Hefeng Li","orcid":"https://orcid.org/0000-0001-8325-6201"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hefeng Li","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088246745"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":1.8485,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85483572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"95","issue":"6-7","first_page":"1114","last_page":"1130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9991000294685364,"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":0.9987999796867371,"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":0.9081846475601196},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6277250051498413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.625842809677124},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6056610345840454},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5887932777404785},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5866076946258545},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.5085078477859497},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5069801807403564},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5035721659660339},{"id":"https://openalex.org/keywords/finite-difference-coefficient","display_name":"Finite difference coefficient","score":0.49987173080444336},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.46703052520751953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4024483263492584},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20046046376228333},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18205642700195312},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.10424721240997314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9081846475601196},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6277250051498413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.625842809677124},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6056610345840454},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5887932777404785},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5866076946258545},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.5085078477859497},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5069801807403564},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5035721659660339},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.49987173080444336},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.46703052520751953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4024483263492584},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20046046376228333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18205642700195312},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.10424721240997314},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1378810","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1378810","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G809826743","display_name":null,"funder_award_id":"11671251","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W902939226","https://openalex.org/W1633484149","https://openalex.org/W1744306136","https://openalex.org/W1963527980","https://openalex.org/W2003734192","https://openalex.org/W2011095781","https://openalex.org/W2034839545","https://openalex.org/W2039427414","https://openalex.org/W2044837570","https://openalex.org/W2158845426","https://openalex.org/W2161397260","https://openalex.org/W2163692138","https://openalex.org/W2172034033","https://openalex.org/W2340358137","https://openalex.org/W2585496935","https://openalex.org/W2605247189","https://openalex.org/W2787959293","https://openalex.org/W2963055256","https://openalex.org/W2963707245","https://openalex.org/W2963763304","https://openalex.org/W2963774931","https://openalex.org/W3103229763"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2372700288","https://openalex.org/W2983915667","https://openalex.org/W2085654163","https://openalex.org/W2392533133","https://openalex.org/W2370641521","https://openalex.org/W2756693448","https://openalex.org/W2376771521","https://openalex.org/W2766501744","https://openalex.org/W2363145727"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,15,25,33,41],"high-dimensional":[4],"Caputo-type":[5],"parabolic":[6],"equation":[7],"with":[8],"fractional":[9],"Laplacian":[10],"is":[11],"studied":[12],"by":[13],"using":[14],"finite":[16,27],"difference":[17,28],"method.":[18],"The":[19],"convergence":[20],"and":[21],"error":[22],"estimate":[23],"of":[24],"established":[26],"scheme":[29],"are":[30,36],"shown.":[31],"And":[32],"illustrative":[34],"examples":[35],"also":[37],"displayed":[38],"which":[39],"support":[40],"theoretical":[42],"analysis.":[43]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}