{"id":"https://openalex.org/W4399794307","doi":"https://doi.org/10.1137/24m162950x","title":"A Simple and Fast Finite Difference Method for the Integral Fractional Laplacian of Variable Order","display_name":"A Simple and Fast Finite Difference Method for the Integral Fractional Laplacian of Variable Order","publication_year":2026,"publication_date":"2026-04-06","ids":{"openalex":"https://openalex.org/W4399794307","doi":"https://doi.org/10.1137/24m162950x"},"language":"en","primary_location":{"id":"doi:10.1137/24m162950x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m162950x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2406.10524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102996133","display_name":"Zhaopeng Hao","orcid":null},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhaopeng Hao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109934387","display_name":"Siyuan Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyuan Shi","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030093874","display_name":"Zhongqiang Zhang","orcid":"https://orcid.org/0000-0001-8032-7510"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhongqiang Zhang","raw_affiliation_strings":["Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609 USA"],"raw_orcid":"https://orcid.org/0000-0001-8032-7510","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609 USA","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000360043","display_name":"Rui Du","orcid":"https://orcid.org/0000-0002-3811-7488"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Du","raw_affiliation_strings":["Corresponding author. School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096 China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102996133"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00175131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"2","first_page":"A748","last_page":"A783"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9959999918937683,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9911999702453613,"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/simple","display_name":"Simple (philosophy)","score":0.7905789613723755},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6583550572395325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6456975936889648},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6059014797210693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5143886208534241},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"Fractional Laplacian","score":0.4652728736400604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.422306627035141},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.41878464818000793},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.06318631768226624}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7905789613723755},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6583550572395325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6456975936889648},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6059014797210693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5143886208534241},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.4652728736400604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.422306627035141},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.41878464818000793},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.06318631768226624},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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":3,"locations":[{"id":"doi:10.1137/24m162950x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m162950x","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:arXiv.org:2406.10524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.10524","pdf_url":"https://arxiv.org/pdf/2406.10524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.2406.10524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2406.10524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2406.10524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.10524","pdf_url":"https://arxiv.org/pdf/2406.10524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G558138960","display_name":null,"funder_award_id":"BK20221450","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320312855","display_name":"Missouri University of Science and Technology","ror":"https://ror.org/00scwqd12"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324856","display_name":"Southeast University","ror":"https://ror.org/04ct4d772"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W4300101996","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W2142393343","https://openalex.org/W2338854850","https://openalex.org/W2184239527"],"abstract_inverted_index":{"For":[0],"the":[1,19,35,48,56,66,79,93],"fractional":[2,38,68,84],"Laplacian":[3,39,85],"of":[4,21,51,78,97],"variable":[5],"order,":[6],"an":[7],"efficient":[8],"and":[9,29,54,86,95,100],"accurate":[10],"numerical":[11,90],"evaluation":[12],"in":[13],"multi-dimension":[14],"is":[15,50],"a":[16,22,27,42,72],"challenge":[17],"for":[18,34,81],"nature":[20],"singular":[23],"integral.":[24,44],"We":[25,45,70],"propose":[26],"simple":[28],"easy-to-implement":[30],"finite":[31,58],"difference":[32,59],"scheme":[33,49,60,80],"multi-dimensional":[36],"variable-order":[37,67,83],"defined":[40],"by":[41],"hypersingular":[43],"prove":[46],"that":[47],"second-order":[52],"convergence":[53],"apply":[55],"developed":[57],"to":[61],"solve":[62],"various":[63],"equations":[64],"with":[65,75],"Laplacian.":[69],"present":[71],"fast":[73],"solver":[74],"quasi-linear":[76],"complexity":[77],"computing":[82],"corresponding":[87],"PDEs.":[88],"Several":[89],"examples":[91],"demonstrate":[92],"accuracy":[94],"efficiency":[96],"our":[98,102],"algorithm":[99],"verify":[101],"theory.":[103]},"counts_by_year":[],"updated_date":"2026-04-08T06:01:36.053099","created_date":"2024-06-19T00:00:00"}