{"id":"https://openalex.org/W2531429468","doi":"https://doi.org/10.1080/00207160.2016.1247442","title":"On a numerical investigation of the time fractional Fokker\u2013 Planck equation via local discontinuous Galerkin method","display_name":"On a numerical investigation of the time fractional Fokker\u2013 Planck equation via local discontinuous Galerkin method","publication_year":2016,"publication_date":"2016-10-15","ids":{"openalex":"https://openalex.org/W2531429468","doi":"https://doi.org/10.1080/00207160.2016.1247442","mag":"2531429468"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2016.1247442","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1247442","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/A5078997412","display_name":"Jafar Eshaghi","orcid":null},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Jafar Eshaghi","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026886970","display_name":"Hojatollah Adibi","orcid":"https://orcid.org/0000-0002-8167-5020"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hojatollah Adibi","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111774530","display_name":"Saeed Kazem","orcid":null},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Saeed Kazem","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026886970"],"corresponding_institution_ids":["https://openalex.org/I158248296"],"apc_list":null,"apc_paid":null,"fwci":0.6833,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73320188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"94","issue":"9","first_page":"1916","last_page":"1942"},"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":0.9969000220298767,"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":0.994700014591217,"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/discretization","display_name":"Discretization","score":0.8779707551002502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7805615663528442},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6442690491676331},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6256324648857117},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6164705157279968},{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.5861409306526184},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5543290972709656},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5490291118621826},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5112752914428711},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4482003152370453},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42754611372947693},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41258448362350464},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.24721744656562805},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1346331536769867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10049805045127869},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08927321434020996}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8779707551002502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7805615663528442},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6442690491676331},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6256324648857117},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6164705157279968},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.5861409306526184},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5543290972709656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5490291118621826},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5112752914428711},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4482003152370453},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42754611372947693},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41258448362350464},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.24721744656562805},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1346331536769867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10049805045127869},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08927321434020996},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2016.1247442","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2016.1247442","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":42,"referenced_works":["https://openalex.org/W49087508","https://openalex.org/W56786142","https://openalex.org/W70071832","https://openalex.org/W431959091","https://openalex.org/W1507767947","https://openalex.org/W1530054495","https://openalex.org/W1550268283","https://openalex.org/W1605182429","https://openalex.org/W1975383112","https://openalex.org/W1975670568","https://openalex.org/W1976076854","https://openalex.org/W1977360274","https://openalex.org/W1981376782","https://openalex.org/W1982560116","https://openalex.org/W1985438383","https://openalex.org/W2006561420","https://openalex.org/W2007866354","https://openalex.org/W2012938047","https://openalex.org/W2036215498","https://openalex.org/W2042923669","https://openalex.org/W2046416768","https://openalex.org/W2055701161","https://openalex.org/W2058524173","https://openalex.org/W2065908448","https://openalex.org/W2074336586","https://openalex.org/W2075551360","https://openalex.org/W2078207410","https://openalex.org/W2081811871","https://openalex.org/W2085848537","https://openalex.org/W2085961649","https://openalex.org/W2092432858","https://openalex.org/W2093685032","https://openalex.org/W2094838226","https://openalex.org/W2104736025","https://openalex.org/W2116807840","https://openalex.org/W2131774555","https://openalex.org/W2187264218","https://openalex.org/W2298847139","https://openalex.org/W2325849220","https://openalex.org/W2397817385","https://openalex.org/W2787959293","https://openalex.org/W3021895250"],"related_works":["https://openalex.org/W2992409218","https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1494630543","https://openalex.org/W4388044880","https://openalex.org/W1965109456","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W2071875410"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"two":[3,105],"numerical":[4],"solutions":[5],"of":[6,29,84,104],"time":[7,121],"fractional":[8,26,38,49],"Fokker\u2013":[9],"Planck":[10],"equations":[11],"(TFFPE)":[12],"based":[13],"on":[14],"the":[15,25,37,45,48,54,62,68,79,85,100],"local":[16],"discontinuous":[17],"Galerkin":[18],"method":[19],"(LDGM).":[20],"Two":[21],"time-discretization":[22],"schemes":[23],"for":[24,73],"order":[27],"part":[28],"TFFPE":[30],"are":[31,115],"investigated.":[32],"The":[33,108],"first":[34],"discretization":[35],"utilizes":[36],"finite":[39],"difference":[40],"scheme":[41,47,65],"(FFDS)":[42],"and":[43,81,102,113,117],"in":[44,75,120],"second":[46],"derivative":[50],"is":[51],"replaced":[52],"by":[53,61],"Volterra":[55],"integral":[56],"equation":[57],"which":[58],"it":[59],"computed":[60],"trapezoidal":[63],"quadrature":[64],"(TQS).":[66],"Then":[67],"LDGM":[69],"has":[70],"been":[71,89,96],"applied":[72],"space-discretization":[74],"both":[76],"schemes.":[77],"Additionally,":[78],"stability":[80],"convergence":[82,103],"analysis":[83],"proposed":[86,106],"methods":[87],"have":[88,95],"discussed.":[90],"Finally":[91],"some":[92],"test":[93],"problems":[94],"investigated":[97],"to":[98],"confirm":[99],"validity":[101],"methods.":[107],"results":[109],"show":[110],"that":[111],"FFDS":[112],"TQS":[114],"2\u2212\u03b1":[116],"second-order":[118],"accurate":[119],"variable,":[122],"respectively.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
