{"id":"https://openalex.org/W2998764539","doi":"https://doi.org/10.1137/19m1245621","title":"An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes","display_name":"An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2998764539","doi":"https://doi.org/10.1137/19m1245621","mag":"2998764539"},"language":"en","primary_location":{"id":"doi:10.1137/19m1245621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245621","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5004001300","display_name":"Xiangcheng Zheng","orcid":"https://orcid.org/0000-0002-6364-9216"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiangcheng Zheng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035053697","display_name":"Hong Wang","orcid":"https://orcid.org/0000-0002-6938-9507"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004001300"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8567,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.89834922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"58","issue":"1","first_page":"330","last_page":"352"},"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":0.9983000159263611,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9947999715805054,"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":0.8780683279037476},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7770693302154541},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.7472531795501709},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5692000985145569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5231717228889465},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.4988112449645996},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.48237767815589905},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.45112743973731995},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44610846042633057},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4451408386230469},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.44202721118927},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4125763773918152},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4120931625366211},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17103669047355652},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0688326358795166}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8780683279037476},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7770693302154541},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.7472531795501709},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5692000985145569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5231717228889465},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.4988112449645996},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.48237767815589905},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.45112743973731995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44610846042633057},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4451408386230469},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.44202721118927},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4125763773918152},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4120931625366211},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17103669047355652},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0688326358795166},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1245621","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245621","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2152170441","display_name":null,"funder_award_id":"DMS-1620194","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8944192383","display_name":null,"funder_award_id":"W911NF-15-1-0562","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1571391776","https://openalex.org/W1966513244","https://openalex.org/W1977360274","https://openalex.org/W2014440479","https://openalex.org/W2021735811","https://openalex.org/W2065390423","https://openalex.org/W2092146111","https://openalex.org/W2127684492","https://openalex.org/W2137696066","https://openalex.org/W2139227432","https://openalex.org/W2234614486","https://openalex.org/W2605402017","https://openalex.org/W2608656286","https://openalex.org/W2963589517","https://openalex.org/W2963907193","https://openalex.org/W3101734045","https://openalex.org/W4250501155"],"related_works":["https://openalex.org/W2022599090","https://openalex.org/W2043312277","https://openalex.org/W4285786600","https://openalex.org/W4281774867","https://openalex.org/W2972622627","https://openalex.org/W3082176452","https://openalex.org/W2045082303","https://openalex.org/W2800311344","https://openalex.org/W2891408003","https://openalex.org/W1851863087"],"abstract_inverted_index":{"We":[0,16],"develop":[1],"a":[2,10,35,60,65,74],"numerical":[3],"method":[4,32,57,71],"for":[5],"the":[6,20,28,31,44,48,52,56,70,83,87],"boundary-value":[7],"problem":[8],"of":[9,51,89],"variable-order":[11],"linear":[12],"space-fractional":[13],"diffusion":[14],"equation.":[15],"prove":[17],"that":[18],"if":[19],"variable":[21],"order":[22],"reduces":[23],"to":[24],"an":[25,39,78],"integer":[26],"at":[27],"boundary,":[29],"then":[30],"discretized":[33,58,72],"on":[34,59,73],"uniform":[36,61],"partition":[37],"has":[38,63,77],"optimal-order":[40,79],"convergence":[41,67,80],"rate":[42,81],"in":[43,82],"$L_\\infty$":[45,84],"norm":[46,85],"under":[47],"smoothness":[49,88],"assumption":[50],"data":[53,90],"only.":[54,91],"Otherwise,":[55],"mesh":[62,76],"only":[64],"suboptimal-order":[66],"rate,":[68],"but":[69],"graded":[75],"assuming":[86],"Numerical":[92],"experiments":[93],"substantiate":[94],"these":[95],"theoretical":[96],"results.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11}],"updated_date":"2026-03-08T08:50:53.379069","created_date":"2025-10-10T00:00:00"}