{"id":"https://openalex.org/W3000618690","doi":"https://doi.org/10.1515/cmam-2019-0042","title":"Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem","display_name":"Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem","publication_year":2020,"publication_date":"2020-01-15","ids":{"openalex":"https://openalex.org/W3000618690","doi":"https://doi.org/10.1515/cmam-2019-0042","mag":"3000618690"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2019-0042","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2019-0042","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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/A5073082206","display_name":"Chaobao Huang","orcid":"https://orcid.org/0000-0003-3554-7885"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chaobao Huang","raw_affiliation_strings":["School of Mathematics and Quantitative Economics , Shandong University of Finance and Economics , Jinan 250014 , P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-3554-7885","affiliations":[{"raw_affiliation_string":"School of Mathematics and Quantitative Economics , Shandong University of Finance and Economics , Jinan 250014 , P. R. China","institution_ids":["https://openalex.org/I59483232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100375355","display_name":"Xiaohui Liu","orcid":"https://orcid.org/0000-0002-2299-9279"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohui Liu","raw_affiliation_strings":["Applied and Computational Mathematics Division , Beijing Computational Science Research Center , Beijing 100193 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied and Computational Mathematics Division , Beijing Computational Science Research Center , Beijing 100193 , P. R. China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061178606","display_name":"Xiangyun Meng","orcid":"https://orcid.org/0000-0001-5327-6068"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangyun Meng","raw_affiliation_strings":["School of Science , Beijing Jiaotong University , Beijing 100044 , P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-5327-6068","affiliations":[{"raw_affiliation_string":"School of Science , Beijing Jiaotong University , Beijing 100044 , P. R. China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044512711","display_name":"Martin Stynes","orcid":"https://orcid.org/0000-0003-2085-7354"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Martin Stynes","raw_affiliation_strings":["Applied and Computational Mathematics Division , Beijing Computational Science Research Center , Beijing 100193 , P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-2085-7354","affiliations":[{"raw_affiliation_string":"Applied and Computational Mathematics Division , Beijing Computational Science Research Center , Beijing 100193 , P. R. China","institution_ids":["https://openalex.org/I4210139958"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044512711"],"corresponding_institution_ids":["https://openalex.org/I4210139958"],"apc_list":null,"apc_paid":null,"fwci":0.8755,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.80771627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"20","issue":"4","first_page":"815","last_page":"825"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9993000030517578,"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"}},{"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5100113153457642},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49968671798706055},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.43720579147338867},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4306516647338867},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4157285988330841},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40242674946784973},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3678143322467804}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5100113153457642},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49968671798706055},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.43720579147338867},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4306516647338867},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4157285988330841},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40242674946784973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3678143322467804}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2019-0042","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2019-0042","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2443433706","display_name":null,"funder_award_id":"11801332","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3296429765","display_name":null,"funder_award_id":"NSAF-U1930402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8966593327","display_name":null,"funder_award_id":"11971259","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":8,"referenced_works":["https://openalex.org/W1560060148","https://openalex.org/W2051245043","https://openalex.org/W2066060749","https://openalex.org/W2081811871","https://openalex.org/W2092440717","https://openalex.org/W2608656286","https://openalex.org/W2963392111","https://openalex.org/W3000311770"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W2051519054","https://openalex.org/W2488633177","https://openalex.org/W2352708639","https://openalex.org/W2083247966","https://openalex.org/W2043702156"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"initial-boundary":[2],"value":[3],"problem,":[4],"whose":[5],"differential":[6],"equation":[7],"contains":[8],"a":[9,68,146,165,183],"sum":[10],"of":[11,70,112,130,161],"fractional":[12,101,133],"time":[13,102],"derivatives":[14,111],"with":[15],"orders":[16],"between":[17],"0":[18],"and":[19,77,98,135,153,159,164],"1,":[20],"is":[21,26,67,143,149,173],"considered.":[22],"Its":[23],"spatial":[24,141],"domain":[25],"<m:math":[27,45,89],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[28,46,90],"<m:msup>":[29],"<m:mrow>":[30,47,50,91],"<m:mo":[31,36,51,58],"stretchy=\"false\">(</m:mo>":[32],"<m:mn>0</m:mn>":[33],"<m:mo>,</m:mo>":[34,54,56],"<m:mn>1</m:mn>":[35,53,94],"stretchy=\"false\">)</m:mo>":[37],"</m:mrow>":[38,60,61,95],"<m:mi>d</m:mi>":[39,48,92],"</m:msup>":[40],"</m:math>":[41,62,96],"{(0,1)^{d}}":[42],"for":[43,127,139],"some":[44],"<m:mo>\u2208</m:mo>":[49],"stretchy=\"false\">{</m:mo>":[52],"<m:mn>2</m:mn>":[55],"<m:mn>3</m:mn>":[57],"stretchy=\"false\">}</m:mo>":[59],"{d\\in\\{1,2,3\\}}":[63],".":[64],"This":[65],"problem":[66,72],"generalisation":[69],"the":[71,110,113,123,128,140,162,178],"considered":[73],"by":[74],"Stynes,":[75],"O\u2019Riordan":[76],"Gracia":[78],"in":[79,151,156,182],"SIAM":[80],"J.":[81],"Numer.":[82],"Anal.":[83],"55":[84],"(2017),":[85],"pp.":[86],"1057\u20131079,":[87],"where":[88],"<m:mo>=</m:mo>":[93],"{d=1}":[97],"only":[99],"one":[100],"derivative":[103,134],"was":[104],"present.":[105],"A":[106,118],"priori":[107],"bounds":[108],"on":[109,145],"unknown":[114],"solution":[115],"are":[116,169,192],"derived.":[117],"finite":[119,137],"difference":[120],"method,":[121],"using":[122],"well-known":[124],"L1":[125],"scheme":[126],"discretisation":[129],"each":[131],"temporal":[132,179],"classical":[136],"differences":[138],"discretisation,":[142],"constructed":[144],"mesh":[147,180],"that":[148],"uniform":[150],"space":[152],"arbitrarily":[154],"graded":[155],"time.":[157],"Stability":[158],"consistency":[160],"method":[163],"sharp":[166],"convergence":[167],"result":[168],"proved;":[170],"hence":[171],"it":[172],"clear":[174],"how":[175],"to":[176],"choose":[177],"grading":[181],"optimal":[184],"way.":[185],"Numerical":[186],"results":[187,191],"supporting":[188],"our":[189],"theoretical":[190],"provided.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
