{"id":"https://openalex.org/W2898158179","doi":"https://doi.org/10.1142/s179396231941006x","title":"L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity","display_name":"L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity","publication_year":2018,"publication_date":"2018-10-26","ids":{"openalex":"https://openalex.org/W2898158179","doi":"https://doi.org/10.1142/s179396231941006x","mag":"2898158179"},"language":"en","primary_location":{"id":"doi:10.1142/s179396231941006x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179396231941006x","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","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/A5026609401","display_name":"Hu Chen","orcid":"https://orcid.org/0000-0003-3297-2747"},"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":"Hu Chen","raw_affiliation_strings":["Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100194, P. R. China"],"affiliations":[{"raw_affiliation_string":"Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100194, P. R. China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080787074","display_name":"Xiaohan Hu","orcid":"https://orcid.org/0009-0001-5992-7543"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohan Hu","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049220773","display_name":"Jincheng Ren","orcid":"https://orcid.org/0000-0003-3556-0975"},"institutions":[{"id":"https://openalex.org/I7726996","display_name":"Henan University of Economic and Law","ror":"https://ror.org/000jtc944","country_code":"CN","type":"education","lineage":["https://openalex.org/I7726996"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jincheng Ren","raw_affiliation_strings":["College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450045, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450045, P. R. China","institution_ids":["https://openalex.org/I7726996"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048964534","display_name":"Tao Sun","orcid":"https://orcid.org/0000-0003-0913-581X"},"institutions":[{"id":"https://openalex.org/I146613903","display_name":"Shanghai Lixin University of Accounting and Finance","ror":"https://ror.org/02g81yf77","country_code":"CN","type":"education","lineage":["https://openalex.org/I146613903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Sun","raw_affiliation_strings":["School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China","institution_ids":["https://openalex.org/I146613903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111634036","display_name":"Yifa Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifa Tang","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"],"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5026609401"],"corresponding_institution_ids":["https://openalex.org/I4210139958"],"apc_list":null,"apc_paid":null,"fwci":0.6391,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.66941543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"01","first_page":"1941006","last_page":"1941006"},"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":0.9994000196456909,"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/T10514","display_name":"Numerical methods in engineering","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7539651393890381},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.739007294178009},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.6931231021881104},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6582879424095154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5146761536598206},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.451140433549881},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43565860390663147},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4280743896961212},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4280101954936981},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4126984477043152},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3919512927532196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10808664560317993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0734645426273346}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7539651393890381},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.739007294178009},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6931231021881104},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6582879424095154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5146761536598206},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.451140433549881},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43565860390663147},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4280743896961212},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4280101954936981},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4126984477043152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3919512927532196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10808664560317993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0734645426273346},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s179396231941006x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s179396231941006x","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5579978329","display_name":null,"funder_award_id":"11601119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"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":19,"referenced_works":["https://openalex.org/W604143053","https://openalex.org/W1963902701","https://openalex.org/W2019543280","https://openalex.org/W2041540906","https://openalex.org/W2066109671","https://openalex.org/W2089854137","https://openalex.org/W2461957976","https://openalex.org/W2503319909","https://openalex.org/W2505920944","https://openalex.org/W2550897446","https://openalex.org/W2608656286","https://openalex.org/W2613163804","https://openalex.org/W2751422907","https://openalex.org/W2756583637","https://openalex.org/W2768802025","https://openalex.org/W2898636786","https://openalex.org/W2916540042","https://openalex.org/W4247953052","https://openalex.org/W4297914047"],"related_works":["https://openalex.org/W2027202866","https://openalex.org/W3149920197","https://openalex.org/W4293569346","https://openalex.org/W2397056152","https://openalex.org/W2494658963","https://openalex.org/W4252904065","https://openalex.org/W3017235236","https://openalex.org/W2949885877","https://openalex.org/W2129544565","https://openalex.org/W2006251942"],"abstract_inverted_index":{"Numerical":[0],"approximation":[1],"for":[2,73],"a":[3,69],"linearized":[4],"time":[5],"fractional":[6,59],"KdV":[7],"equation":[8],"with":[9,39],"initial":[10],"singularity":[11],"using":[12],"[Formula:":[13,27,34,47,50],"see":[14,28,35,48,51],"text]":[15,29,36,49,52],"scheme":[16,30,65],"on":[17],"graded":[18],"mesh":[19],"is":[20,23,53,66],"considered.":[21],"It":[22],"proved":[24],"that":[25],"the":[26,43,54,74,92,97,100],"can":[31],"attain":[32],"order":[33,55],"convergence":[37,81],"rate":[38],"appropriate":[40],"choice":[41],"of":[42,56,99],"grading":[44],"parameter,":[45],"where":[46],"temporal":[57],"Caputo":[58],"derivative.":[60],"A":[61],"fully":[62],"discrete":[63],"spectral":[64,71],"constructed":[67],"combing":[68],"Petrov\u2013Galerkin":[70],"method":[72],"spatial":[75],"discretization,":[76],"and":[77,80,95],"its":[78],"stability":[79],"are":[82,88],"theoretically":[83],"proved.":[84],"Some":[85],"numerical":[86],"results":[87],"provided":[89],"to":[90],"verify":[91],"theoretical":[93],"analysis":[94],"demonstrated":[96],"sharpness":[98],"error":[101],"analysis.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
