{"id":"https://openalex.org/W2644048988","doi":"https://doi.org/10.1080/00207160.2017.1346243","title":"An efficient method based on the second kind Chebyshev wavelets for solving variable-order fractional convection diffusion equations","display_name":"An efficient method based on the second kind Chebyshev wavelets for solving variable-order fractional convection diffusion equations","publication_year":2017,"publication_date":"2017-06-23","ids":{"openalex":"https://openalex.org/W2644048988","doi":"https://doi.org/10.1080/00207160.2017.1346243","mag":"2644048988"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1346243","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1346243","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/A5048488969","display_name":"Mingxu Yi","orcid":"https://orcid.org/0000-0001-8279-1691"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingxu Yi","raw_affiliation_strings":["School of Aeronautic Science and Technology, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Technology, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048523374","display_name":"Yunpeng Ma","orcid":"https://orcid.org/0000-0002-7067-1980"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunpeng Ma","raw_affiliation_strings":["School of Aeronautic Science and Technology, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Technology, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100755772","display_name":"Lifeng Wang","orcid":"https://orcid.org/0000-0001-5051-5991"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lifeng Wang","raw_affiliation_strings":["School of Aeronautic Science and Technology, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Technology, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100755772"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":0.4643,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61356707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"95","issue":"10","first_page":"1973","last_page":"1991"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9918000102043152,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.7758113741874695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7666603326797485},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.6567612886428833},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.6505058407783508},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6368215084075928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5287662744522095},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.5160855650901794},{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.49219074845314026},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.484894335269928},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.47740116715431213},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.46363064646720886},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42478129267692566},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.42385879158973694},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41577935218811035},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3257249593734741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14481854438781738},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.143336683511734},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.0961344838142395},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.08548009395599365}],"concepts":[{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.7758113741874695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7666603326797485},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.6567612886428833},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6505058407783508},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6368215084075928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5287662744522095},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.5160855650901794},{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.49219074845314026},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.484894335269928},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.47740116715431213},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.46363064646720886},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42478129267692566},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.42385879158973694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41577935218811035},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3257249593734741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14481854438781738},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.143336683511734},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0961344838142395},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.08548009395599365},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1346243","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1346243","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1971743075","https://openalex.org/W1973096509","https://openalex.org/W1984200508","https://openalex.org/W1990956480","https://openalex.org/W1991610336","https://openalex.org/W1992057522","https://openalex.org/W2009446705","https://openalex.org/W2011253853","https://openalex.org/W2014042268","https://openalex.org/W2021735811","https://openalex.org/W2027955822","https://openalex.org/W2048618474","https://openalex.org/W2054138202","https://openalex.org/W2066229481","https://openalex.org/W2071033102","https://openalex.org/W2083828525","https://openalex.org/W2093820071","https://openalex.org/W2098263458","https://openalex.org/W2107162131","https://openalex.org/W2186354574"],"related_works":["https://openalex.org/W2626380860","https://openalex.org/W2090151895","https://openalex.org/W2054912819","https://openalex.org/W2593423823","https://openalex.org/W1735526525","https://openalex.org/W2103708249","https://openalex.org/W2270587440","https://openalex.org/W2106962382","https://openalex.org/W2412589306","https://openalex.org/W3124846489"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"class":[4],"of":[5,16,27,77,93,104],"variable-order":[6,28],"fractional":[7,29],"convection":[8],"diffusion":[9],"equations":[10,55],"have":[11],"been":[12],"solved":[13,67],"with":[14],"assistance":[15],"the":[17,34,41,49,53,60,74,78,83,100,105],"second":[18,35,42],"kind":[19,36,43],"Chebyshev":[20,37,44],"wavelets":[21,45],"operational":[22,25,51],"matrix.":[23],"The":[24],"matrix":[26],"derivative":[30],"is":[31],"derived":[32],"for":[33],"wavelets.":[38],"By":[39],"implementing":[40],"functions":[46],"and":[47,86,102],"also":[48],"associated":[50],"matrix,":[52],"considered":[54,97],"will":[56],"be":[57,66],"reduced":[58],"to":[59,82,98],"corresponding":[61],"Sylvester":[62],"equation,":[63],"which":[64],"can":[65],"by":[68],"some":[69],"appropriate":[70],"iterative":[71],"solvers.":[72],"Also,":[73],"convergence":[75],"analysis":[76],"proposed":[79],"numerical":[80,94],"method":[81],"exact":[84],"solutions":[85],"error":[87],"estimation":[88],"are":[89,96],"given.":[90],"A":[91],"variety":[92],"examples":[95],"show":[99],"efficiency":[101],"accuracy":[103],"presented":[106],"technique.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
