{"id":"https://openalex.org/W1964804260","doi":"https://doi.org/10.1137/110840959","title":"Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation","display_name":"Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1964804260","doi":"https://doi.org/10.1137/110840959","mag":"1964804260"},"language":"en","primary_location":{"id":"doi:10.1137/110840959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110840959","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/A5100415499","display_name":"Yanan Zhang","orcid":"https://orcid.org/0000-0001-8280-6419"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ya-nan Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080921775","display_name":"Zhi\u2010zhong Sun","orcid":"https://orcid.org/0000-0003-2994-1368"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhi-zhong Sun","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065261052","display_name":"Xuan Zhao","orcid":"https://orcid.org/0000-0003-3763-3920"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuan Zhao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100415499"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.8596,"has_fulltext":false,"cited_by_count":175,"citation_normalized_percentile":{"value":0.99352611,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"50","issue":"3","first_page":"1535","last_page":"1555"},"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":0.9991000294685364,"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":0.9968000054359436,"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":0.8373994827270508},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.7073870897293091},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6707367300987244},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5437203645706177},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5404605865478516},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5361788868904114},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.4951561987400055},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4916420578956604},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4828825294971466},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46669939160346985},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4372240900993347},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36324578523635864},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.34107863903045654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8373994827270508},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.7073870897293091},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6707367300987244},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5437203645706177},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5404605865478516},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5361788868904114},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.4951561987400055},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4916420578956604},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4828825294971466},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46669939160346985},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4372240900993347},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36324578523635864},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.34107863903045654},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110840959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110840959","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W110340196","https://openalex.org/W171286733","https://openalex.org/W1502589723","https://openalex.org/W1969312973","https://openalex.org/W1970546830","https://openalex.org/W1973950856","https://openalex.org/W1974258811","https://openalex.org/W1977696410","https://openalex.org/W1980154613","https://openalex.org/W1984091802","https://openalex.org/W1992207080","https://openalex.org/W1995597760","https://openalex.org/W2005179009","https://openalex.org/W2009239825","https://openalex.org/W2012021517","https://openalex.org/W2012163408","https://openalex.org/W2021735811","https://openalex.org/W2030146312","https://openalex.org/W2033471049","https://openalex.org/W2034839545","https://openalex.org/W2038588805","https://openalex.org/W2041827099","https://openalex.org/W2047594597","https://openalex.org/W2056829543","https://openalex.org/W2057206818","https://openalex.org/W2057769307","https://openalex.org/W2062517214","https://openalex.org/W2067855936","https://openalex.org/W2073659542","https://openalex.org/W2081531908","https://openalex.org/W2083834253","https://openalex.org/W2083955243","https://openalex.org/W2092718516","https://openalex.org/W2099330130","https://openalex.org/W2104736025","https://openalex.org/W2109328281","https://openalex.org/W2111271983","https://openalex.org/W2119671522","https://openalex.org/W2123103679","https://openalex.org/W2165076033","https://openalex.org/W2490605950","https://openalex.org/W2787959293"],"related_works":["https://openalex.org/W2043555141","https://openalex.org/W2952782738","https://openalex.org/W1987868570","https://openalex.org/W2048336173","https://openalex.org/W2326356320","https://openalex.org/W4253925511","https://openalex.org/W2042502646","https://openalex.org/W3163291216","https://openalex.org/W1855971808","https://openalex.org/W2045374466"],"abstract_inverted_index":{"In":[0,89],"this":[1],"paper,":[2],"we":[3],"consider":[4],"the":[5,10,28,36,43,58,72,83,98,117,122],"numerical":[6],"method":[7,41],"for":[8,32],"solving":[9],"two-dimensional":[11],"fractional":[12,18],"diffusion-wave":[13],"equation":[14],"with":[15],"a":[16,91],"time":[17,44,127],"derivative":[19],"of":[20,57],"order":[21,65],"$\\alpha$":[22],"($1<\\alpha<2$).":[23],"A":[24],"difference":[25,30],"scheme":[26,59,94,120],"combining":[27],"compact":[29,118],"approach":[31],"spatial":[33,79],"discretization":[34],"and":[35,48,53,76,85,97,114,125],"alternating":[37],"direction":[38],"implicit":[39],"(ADI)":[40],"in":[42,82],"stepping":[45],"is":[46,66,71,95],"proposed":[47],"analyzed.":[49],"The":[50,63],"unconditional":[51],"stability":[52],"$H^1$":[54],"norm":[55],"convergence":[56,64],"are":[60,78,102,107],"proved":[61],"rigorously.":[62],"$\\mathcal":[67],"{O}(\\tau^{3-\\alpha}+h_1^4+h^4_2),$":[68],"where":[69],"$\\tau$":[70],"temporal":[73],"grid":[74,80],"size":[75],"$h_1,h_2$":[77],"sizes":[81],"$x$":[84],"$y$":[86],"directions,":[87],"respectively.":[88],"addition,":[90],"Crank--Nicolson":[92],"ADI":[93,119],"presented":[96,108],"corresponding":[99],"error":[100],"estimates":[101],"also":[103],"established.":[104],"Numerical":[105],"results":[106],"to":[109],"support":[110],"our":[111],"theoretical":[112],"analysis":[113],"indicate":[115],"that":[116],"reduces":[121],"storage":[123],"requirement":[124],"CPU":[126],"successfully.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}