{"id":"https://openalex.org/W2611074852","doi":"https://doi.org/10.1080/00207160.2017.1324150","title":"Orthogonal spline collocation scheme for the multi-term time-fractional diffusion equation","display_name":"Orthogonal spline collocation scheme for the multi-term time-fractional diffusion equation","publication_year":2017,"publication_date":"2017-05-02","ids":{"openalex":"https://openalex.org/W2611074852","doi":"https://doi.org/10.1080/00207160.2017.1324150","mag":"2611074852"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1324150","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1324150","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/A5039089697","display_name":"Leijie Qiao","orcid":"https://orcid.org/0000-0003-3659-8588"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Leijie Qiao","raw_affiliation_strings":["Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100778599","display_name":"Da Xu","orcid":"https://orcid.org/0000-0002-6283-2123"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Da Xu","raw_affiliation_strings":["Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039089697"],"corresponding_institution_ids":["https://openalex.org/I173759888"],"apc_list":null,"apc_paid":null,"fwci":2.3106,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88082421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"95","issue":"8","first_page":"1478","last_page":"1493"},"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":0.9957000017166138,"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":0.9944000244140625,"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":0.7907373905181885},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.7186636328697205},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5863621234893799},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5729899406433105},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5592719316482544},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5513092875480652},{"id":"https://openalex.org/keywords/m-spline","display_name":"M-spline","score":0.5070333480834961},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4916990399360657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4836500883102417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.482983261346817},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.4649824798107147},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4621383249759674},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.442109078168869},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.44078612327575684},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.43392571806907654},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4134778678417206},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.3841734230518341},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3633490204811096},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1955711543560028},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.11373540759086609},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10958191752433777},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.06538593769073486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7907373905181885},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.7186636328697205},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5863621234893799},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5729899406433105},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5592719316482544},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5513092875480652},{"id":"https://openalex.org/C199765470","wikidata":"https://www.wikidata.org/wiki/Q6712116","display_name":"M-spline","level":5,"score":0.5070333480834961},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4916990399360657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4836500883102417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.482983261346817},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.4649824798107147},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4621383249759674},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.442109078168869},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.44078612327575684},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.43392571806907654},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4134778678417206},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.3841734230518341},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3633490204811096},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1955711543560028},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.11373540759086609},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10958191752433777},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.06538593769073486},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"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/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"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/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1324150","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1324150","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":[{"id":"https://openalex.org/G3438589314","display_name":null,"funder_award_id":"11671131","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W577962163","https://openalex.org/W1482513797","https://openalex.org/W1584611818","https://openalex.org/W1891757183","https://openalex.org/W1965890696","https://openalex.org/W1969312973","https://openalex.org/W1972900338","https://openalex.org/W1978383541","https://openalex.org/W1979551969","https://openalex.org/W1980154613","https://openalex.org/W1981709692","https://openalex.org/W1986208932","https://openalex.org/W1996143385","https://openalex.org/W1998312161","https://openalex.org/W2004097100","https://openalex.org/W2030146312","https://openalex.org/W2034850563","https://openalex.org/W2035738465","https://openalex.org/W2036044118","https://openalex.org/W2039174185","https://openalex.org/W2041540906","https://openalex.org/W2046101570","https://openalex.org/W2051245043","https://openalex.org/W2053796073","https://openalex.org/W2059607966","https://openalex.org/W2065201216","https://openalex.org/W2066060749","https://openalex.org/W2076112708","https://openalex.org/W2078003747","https://openalex.org/W2081468400","https://openalex.org/W2081811871","https://openalex.org/W2093225350","https://openalex.org/W2093685032","https://openalex.org/W2099266473","https://openalex.org/W2101930273","https://openalex.org/W2165076033","https://openalex.org/W2168458035","https://openalex.org/W2338894593","https://openalex.org/W2732661672","https://openalex.org/W2787959293","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2012938622","https://openalex.org/W2094336842","https://openalex.org/W2186192279","https://openalex.org/W1979498295","https://openalex.org/W2357522173","https://openalex.org/W2383522839","https://openalex.org/W2385811782","https://openalex.org/W2036192383","https://openalex.org/W2213441607","https://openalex.org/W1989277673"],"abstract_inverted_index":{"A":[0],"novel":[1],"numerical":[2,39],"technique":[3],"is":[4,20],"considered":[5],"for":[6,22,41],"the":[7],"solution":[8],"of":[9],"a":[10,26],"multi-term":[11],"time-fractional":[12],"diffusion":[13],"equation.":[14],"The":[15,32,38],"orthogonal":[16],"spline":[17],"collocation":[18],"method":[19,29],"used":[21],"in":[23,30],"space,":[24],"and":[25,34,43],"finite":[27],"difference":[28],"time.":[31],"stability":[33],"convergence":[35],"are":[36],"provided.":[37],"experiments":[40],"one":[42],"two":[44],"dimensional":[45],"problems":[46],"support":[47],"our":[48],"theoretical":[49],"analysis.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
