{"id":"https://openalex.org/W4404724348","doi":"https://doi.org/10.1002/nla.2605","title":"An IRK\u2010QCD Scheme for the Space Fractional Diffusion Equation and Block\u2010Lower\u2010Triangle Preconditioners for the Corresponding Linear Systems","display_name":"An IRK\u2010QCD Scheme for the Space Fractional Diffusion Equation and Block\u2010Lower\u2010Triangle Preconditioners for the Corresponding Linear Systems","publication_year":2024,"publication_date":"2024-11-26","ids":{"openalex":"https://openalex.org/W4404724348","doi":"https://doi.org/10.1002/nla.2605"},"language":"en","primary_location":{"id":"doi:10.1002/nla.2605","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2605","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2605","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2605","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072377026","display_name":"Zi\u2010Hang She","orcid":"https://orcid.org/0000-0001-9274-037X"},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]},{"id":"https://openalex.org/I4210165736","display_name":"Hanshan Normal University","ror":"https://ror.org/05tqaz865","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165736"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zi\u2010Hang She","raw_affiliation_strings":["Department of Mathematics Hanshan Normal University  Chaozhou China","Department of Mathematics Shantou University  Shantou China","Department of Mathematics, Shantou University, Shantou, China","Department of Mathematics, Hanshan Normal University, Chaozhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Hanshan Normal University  Chaozhou China","institution_ids":["https://openalex.org/I4210165736"]},{"raw_affiliation_string":"Department of Mathematics Shantou University  Shantou China","institution_ids":["https://openalex.org/I32574673"]},{"raw_affiliation_string":"Department of Mathematics, Shantou University, Shantou, China","institution_ids":["https://openalex.org/I32574673"]},{"raw_affiliation_string":"Department of Mathematics, Hanshan Normal University, Chaozhou, China","institution_ids":["https://openalex.org/I4210165736"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051844247","display_name":"Yi\u2010Feng Qiu","orcid":"https://orcid.org/0000-0002-2747-9598"},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi\u2010Feng Qiu","raw_affiliation_strings":["Department of Mathematics Shantou University  Shantou China","Department of Mathematics, Shantou University, Shantou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Shantou University  Shantou China","institution_ids":["https://openalex.org/I32574673"]},{"raw_affiliation_string":"Department of Mathematics, Shantou University, Shantou, China","institution_ids":["https://openalex.org/I32574673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100385745","display_name":"Xu Chen","orcid":"https://orcid.org/0000-0002-9241-7350"},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Chen","raw_affiliation_strings":["School of Economics Guangdong University of Technology  Guangzhou China","School of Economics, Guangdong University of Technology, Guangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics Guangdong University of Technology  Guangzhou China","institution_ids":["https://openalex.org/I139024713"]},{"raw_affiliation_string":"School of Economics, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051090230","display_name":"Fu\u2010Rong Lin","orcid":"https://orcid.org/0000-0003-4099-6706"},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fu\u2010Rong Lin","raw_affiliation_strings":["Department of Mathematics Shantou University  Shantou China","Department of Mathematics, Shantou University, Shantou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Shantou University  Shantou China","institution_ids":["https://openalex.org/I32574673"]},{"raw_affiliation_string":"Department of Mathematics, Shantou University, Shantou, China","institution_ids":["https://openalex.org/I32574673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051090230"],"corresponding_institution_ids":["https://openalex.org/I32574673"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.2981,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54833897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"32","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9958000183105469,"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":0.7957583665847778},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5956717133522034},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5392858386039734},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5059260725975037},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44093963503837585},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43384936451911926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3684995770454407},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19527602195739746},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09809237718582153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07629251480102539},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.050316959619522095}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7957583665847778},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5956717133522034},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5392858386039734},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5059260725975037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44093963503837585},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43384936451911926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3684995770454407},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19527602195739746},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09809237718582153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07629251480102539},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.050316959619522095},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nla.2605","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2605","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2605","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/nla.2605","is_oa":true,"landing_page_url":"https://doi.org/10.1002/nla.2605","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nla.2605","source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5528738210","display_name":null,"funder_award_id":"12101137","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8337130706","display_name":null,"funder_award_id":"12301481","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"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404724348.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W221829734","https://openalex.org/W1436001274","https://openalex.org/W1506342804","https://openalex.org/W1514337951","https://openalex.org/W1625478003","https://openalex.org/W1983959946","https://openalex.org/W1989955731","https://openalex.org/W1995504856","https://openalex.org/W1998561306","https://openalex.org/W2001011967","https://openalex.org/W2005041367","https://openalex.org/W2013336356","https://openalex.org/W2014666630","https://openalex.org/W2037274488","https://openalex.org/W2042388195","https://openalex.org/W2047954521","https://openalex.org/W2054899953","https://openalex.org/W2055148154","https://openalex.org/W2055846437","https://openalex.org/W2057119166","https://openalex.org/W2062092992","https://openalex.org/W2068610405","https://openalex.org/W2092912961","https://openalex.org/W2094838226","https://openalex.org/W2099111135","https://openalex.org/W2104736025","https://openalex.org/W2105723279","https://openalex.org/W2107162131","https://openalex.org/W2118072570","https://openalex.org/W2118160506","https://openalex.org/W2125366357","https://openalex.org/W2127769310","https://openalex.org/W2138935277","https://openalex.org/W2139948151","https://openalex.org/W2152287259","https://openalex.org/W2587904726","https://openalex.org/W2595107927","https://openalex.org/W2601947471","https://openalex.org/W2744463887","https://openalex.org/W2776784679","https://openalex.org/W2791197185","https://openalex.org/W2912676564","https://openalex.org/W2947970829","https://openalex.org/W2955219381","https://openalex.org/W3099167587","https://openalex.org/W3103086007","https://openalex.org/W3105813679","https://openalex.org/W3125886675","https://openalex.org/W3161565236","https://openalex.org/W4240596267","https://openalex.org/W4303629077"],"related_works":["https://openalex.org/W1975289146","https://openalex.org/W2105887828","https://openalex.org/W2122599759","https://openalex.org/W4236520801","https://openalex.org/W2372403409","https://openalex.org/W4242726756","https://openalex.org/W1537234410","https://openalex.org/W1995022398","https://openalex.org/W2484602794","https://openalex.org/W3021755553"],"abstract_inverted_index":{"ABSTRACT":[0],"In":[1],"this":[2],"paper,":[3],"a":[4,52,130],"novel":[5],"high\u2010order":[6],"finite":[7],"difference":[8,20,37],"scheme":[9,84],"with":[10],"temporally":[11],"and":[12,27,75,115,146],"spatially":[13],"fourth\u2010order":[14],"accuracy,":[15],"called":[16],"the":[17,35,44,69,76,82,94,101,104,122,126,144,149],"implicit":[18,61],"Runge\u2010Kutta\u2010quasi\u2010compact":[19],"(IRK\u2010QCD)":[21],"scheme,":[22],"is":[23,40,65],"proposed":[24,150],"for":[25,93],"one\u2010":[26],"two\u2010dimensional":[28],"space":[29,45],"fractional":[30,47,116],"diffusion":[31],"equations":[32,57],"(SFDEs).":[33],"Firstly,":[34],"quasi\u2010compact":[36],"(QCD)":[38],"operator":[39],"used":[41],"to":[42,67,142],"approximate":[43],"Riemann\u2010Liouville":[46],"derivative,":[48],"which":[49],"results":[50],"in":[51,108],"system":[53],"of":[54,81,103,112,125,148],"ordinary":[55],"differential":[56],"(ODEs).":[58],"Then":[59],"an":[60,137],"Runge\u2010Kutta":[62],"(IRK)":[63],"method":[64],"applied":[66],"discretize":[68],"resulted":[70],"ODEs.":[71],"The":[72],"unconditionally":[73],"stability":[74],"fourth":[77],"order":[78],"convergence":[79],"rate":[80],"IRK\u2010QCD":[83],"are":[85,91,140],"theoretically":[86],"established.":[87],"Block\u2010lower\u2010triangular":[88],"(BLT)":[89],"preconditioners":[90],"employed":[92],"discretization":[95,113],"linear":[96],"systems.":[97],"We":[98,118],"prove":[99,120],"that":[100,121],"eigenvalues":[102],"preconditioned":[105,127],"matrix":[106,128],"lie":[107],"disc":[109],",":[110],"independent":[111],"step\u2010sizes":[114],"order(s).":[117],"also":[119],"condition":[123],"number":[124],"has":[129],"uniform":[131],"upper":[132],"bound.":[133],"Numerical":[134],"experiments,":[135],"including":[136],"empirical":[138],"example,":[139],"implemented":[141],"illustrate":[143],"accuracy":[145],"efficiency":[147],"method.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}