{"id":"https://openalex.org/W2331832193","doi":"https://doi.org/10.1080/00207160.2016.1148814","title":"Improved efficient difference method for the modified anomalous sub-diffusion equation with a nonlinear source term","display_name":"Improved efficient difference method for the modified anomalous sub-diffusion equation with a nonlinear source term","publication_year":2016,"publication_date":"2016-02-06","ids":{"openalex":"https://openalex.org/W2331832193","doi":"https://doi.org/10.1080/00207160.2016.1148814","mag":"2331832193"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2016.1148814","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1148814","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5100461858","display_name":"Yunfei Li","orcid":"https://orcid.org/0000-0002-0441-0643"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunfei Li","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037198617","display_name":"Dongling Wang","orcid":"https://orcid.org/0000-0001-8509-2837"},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dongling Wang","raw_affiliation_strings":["Department of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an, Shaanxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I37802460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037198617"],"corresponding_institution_ids":["https://openalex.org/I37802460"],"apc_list":null,"apc_paid":null,"fwci":1.8222,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84529046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"94","issue":"4","first_page":"821","last_page":"840"},"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":0.9962999820709229,"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":0.9950000047683716,"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":0.8537551760673523},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.738569974899292},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.59716796875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5787462592124939},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5763754844665527},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5624964237213135},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5532156229019165},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.536584198474884},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48818522691726685},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46004346013069153},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44608229398727417},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4380202293395996},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4289478659629822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8537551760673523},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.738569974899292},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.59716796875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5787462592124939},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5763754844665527},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5624964237213135},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5532156229019165},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.536584198474884},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48818522691726685},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46004346013069153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44608229398727417},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4380202293395996},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4289478659629822},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2016.1148814","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1148814","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":36,"referenced_works":["https://openalex.org/W1584611818","https://openalex.org/W1963580797","https://openalex.org/W1963902701","https://openalex.org/W1966513244","https://openalex.org/W1975605247","https://openalex.org/W1977696410","https://openalex.org/W1980154613","https://openalex.org/W1980593821","https://openalex.org/W1987317750","https://openalex.org/W2001011967","https://openalex.org/W2001031344","https://openalex.org/W2003437637","https://openalex.org/W2012163408","https://openalex.org/W2019543280","https://openalex.org/W2025827119","https://openalex.org/W2030146312","https://openalex.org/W2033402214","https://openalex.org/W2034839545","https://openalex.org/W2038588805","https://openalex.org/W2042993252","https://openalex.org/W2046898057","https://openalex.org/W2056061743","https://openalex.org/W2057769307","https://openalex.org/W2062266804","https://openalex.org/W2065647211","https://openalex.org/W2067040719","https://openalex.org/W2086512227","https://openalex.org/W2092718516","https://openalex.org/W2107162131","https://openalex.org/W2111271983","https://openalex.org/W2158972649","https://openalex.org/W2476959674","https://openalex.org/W2786091816","https://openalex.org/W2787959293","https://openalex.org/W3044006004","https://openalex.org/W3103086007"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W2122344339","https://openalex.org/W4388482258","https://openalex.org/W3114093281","https://openalex.org/W4220931593","https://openalex.org/W4295736060","https://openalex.org/W2034966818","https://openalex.org/W2193950510","https://openalex.org/W2318783616"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"an":[5],"improved":[6],"efficient":[7],"difference":[8,27,31],"method":[9,98,123],"to":[10,34,73,85,107,143],"solve":[11,74],"the":[12,36,41,46,59,64,75,88,97,102,115,129,136,145],"modified":[13],"anomalous":[14],"sub-diffusion":[15],"equation":[16],"with":[17,87,128],"a":[18,79],"nonlinear":[19,89],"source":[20,90],"term.":[21,91],"The":[22,92,121],"weighted":[23],"and":[24,29,40,78,94,101,112,117,132],"shifted":[25],"Gr\u00fcnwald":[26],"operator":[28],"compact":[30],"are":[32,99,141],"used":[33,84],"approximate":[35],"Riemann\u2013Liouville":[37],"fractional":[38],"derivative":[39],"space":[42,53,60,118],"derivative,":[43],"respectively.":[44],"Since":[45],"semi-discrete":[47,76],"system":[48,77],"obtained":[49],"by":[50],"discretizing":[51],"in":[52,135],"has":[54,124],"some":[55],"stiff":[56],"properties":[57],"when":[58],"mesh":[61],"is":[62,70,83,105],"dense,":[63],"second-order":[65,80],"backward":[66],"differentiation":[67],"formula":[68,82],"(BDF)":[69],"then":[71],"employed":[72],"interpolation":[81],"deal":[86],"stability":[93,134],"convergence":[95,103],"of":[96],"discussed":[100],"order":[104],"shown":[106],"be":[108],"O(\u03c42+h4),":[109],"where":[110],"\u03c4":[111],"h":[113],"denote":[114],"time":[116],"step":[119],"size.":[120],"new":[122],"higher":[125],"accuracy":[126],"compared":[127],"existed":[130],"methods":[131],"good":[133],"numerical":[137],"performance.":[138],"Numerical":[139],"examples":[140],"given":[142],"illustrate":[144],"theoretical":[146],"results.":[147]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}