{"id":"https://openalex.org/W3011871526","doi":"https://doi.org/10.1080/00207160.2020.1741556","title":"Discrete-time orthogonal spline collocation method for a modified anomalous diffusion equation","display_name":"Discrete-time orthogonal spline collocation method for a modified anomalous diffusion equation","publication_year":2020,"publication_date":"2020-03-12","ids":{"openalex":"https://openalex.org/W3011871526","doi":"https://doi.org/10.1080/00207160.2020.1741556","mag":"3011871526"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2020.1741556","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1741556","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/A5101670520","display_name":"Haixiang Zhang","orcid":"https://orcid.org/0000-0001-9534-1446"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haixiang Zhang","raw_affiliation_strings":["School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China","institution_ids":["https://openalex.org/I49934816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070696600","display_name":"Xuehua Yang","orcid":"https://orcid.org/0000-0003-1711-6117"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuehua Yang","raw_affiliation_strings":["School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China","institution_ids":["https://openalex.org/I49934816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088635276","display_name":"Qiong Tang","orcid":"https://orcid.org/0000-0002-4021-0403"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiong Tang","raw_affiliation_strings":["School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Hunan University of Technology, Zhuzhou, People's Republic of China","institution_ids":["https://openalex.org/I49934816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070696600"],"corresponding_institution_ids":["https://openalex.org/I49934816"],"apc_list":null,"apc_paid":null,"fwci":0.0678,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42177126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"98","issue":"2","first_page":"288","last_page":"304"},"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":0.9937999844551086,"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/T11416","display_name":"Numerical methods for differential equations","score":0.987500011920929,"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/mathematics","display_name":"Mathematics","score":0.7747571468353271},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6216474771499634},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5445168614387512},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5029696822166443},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.4994947910308838},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.49843263626098633},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48779183626174927},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4810338616371155},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.38449251651763916},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.21728545427322388},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.19324490427970886},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14214926958084106},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.10920169949531555},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10241615772247314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7747571468353271},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6216474771499634},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5445168614387512},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5029696822166443},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.4994947910308838},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.49843263626098633},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48779183626174927},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4810338616371155},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.38449251651763916},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.21728545427322388},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.19324490427970886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14214926958084106},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.10920169949531555},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10241615772247314},{"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/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2020.1741556","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1741556","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":[{"id":"https://metadata.un.org/sdg/15","score":0.47999998927116394,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G1639500526","display_name":null,"funder_award_id":"2018M631403","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2550972485","display_name":null,"funder_award_id":"YB2016B033","funder_id":"https://openalex.org/F4320333642","funder_display_name":"Scientific Research Foundation of Hunan Provincial Education Department"},{"id":"https://openalex.org/G3941454223","display_name":null,"funder_award_id":"11601144","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4612858409","display_name":null,"funder_award_id":"2018JJ3108","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5286204705","display_name":null,"funder_award_id":"2018JJ3109","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5465511826","display_name":null,"funder_award_id":"2018JJ4062","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5910556138","display_name":null,"funder_award_id":"11701168","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8371403372","display_name":null,"funder_award_id":"18B304","funder_id":"https://openalex.org/F4320333642","funder_display_name":"Scientific Research Foundation of Hunan Provincial Education Department"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320333642","display_name":"Scientific Research Foundation of Hunan Provincial Education Department","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1496528431","https://openalex.org/W1872704448","https://openalex.org/W1891757183","https://openalex.org/W1996576314","https://openalex.org/W2001011967","https://openalex.org/W2001031344","https://openalex.org/W2013285173","https://openalex.org/W2025827119","https://openalex.org/W2032443585","https://openalex.org/W2033402214","https://openalex.org/W2033593438","https://openalex.org/W2034850563","https://openalex.org/W2046740511","https://openalex.org/W2054602319","https://openalex.org/W2057769307","https://openalex.org/W2067040719","https://openalex.org/W2073463903","https://openalex.org/W2079050082","https://openalex.org/W2086512227","https://openalex.org/W2111271983","https://openalex.org/W2125366357","https://openalex.org/W2158972649","https://openalex.org/W2172194806","https://openalex.org/W2286079127","https://openalex.org/W2330592385","https://openalex.org/W2468196072","https://openalex.org/W2782132367","https://openalex.org/W2790820636","https://openalex.org/W2793446492","https://openalex.org/W2898158179","https://openalex.org/W2910660763","https://openalex.org/W2947286017","https://openalex.org/W2991277276","https://openalex.org/W3044006004"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W1987365920","https://openalex.org/W2889856026","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"The":[0,46],"modified":[1],"anomalous":[2,11],"sub-diffusion":[3],"equation":[4],"(MASDE)":[5],"describes":[6],"processes":[7],"that":[8],"become":[9],"less":[10],"as":[12],"time":[13],"progresses.":[14],"In":[15],"this":[16],"paper,":[17],"based":[18],"on":[19],"Crank-Nicolson":[20],"and":[21,23,40,48],"weighted":[22],"shifted":[24],"Gr\u00fcnwald":[25],"difference":[26],"(WSGD)":[27],"formula,":[28],"we":[29],"develop":[30],"orthogonal":[31],"spline":[32],"collocation":[33],"(OSC)":[34],"method":[35],"with":[36,64],"second-order":[37],"temporal":[38],"accuracy":[39,43],"fourth-order":[41],"spatial":[42],"for":[44],"MASDE.":[45],"stability":[47],"convergence":[49],"of":[50],"our":[51,59,65],"numerical":[52,60],"schemes":[53],"are":[54,62],"analysed":[55],"in":[56],"detail.":[57],"Also,":[58],"results":[61],"consistent":[63],"theoretical":[66],"analysis.":[67]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
