{"id":"https://openalex.org/W3000544683","doi":"https://doi.org/10.1007/s11786-019-00448-x","title":"High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations","display_name":"High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations","publication_year":2020,"publication_date":"2020-01-16","ids":{"openalex":"https://openalex.org/W3000544683","doi":"https://doi.org/10.1007/s11786-019-00448-x","mag":"3000544683"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-019-00448-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-019-00448-x","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/1822/66733","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019735617","display_name":"L. L. Ferr\u00e1s","orcid":"https://orcid.org/0000-0001-5477-3226"},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Lu\u00eds L. Ferr\u00e1s","raw_affiliation_strings":["Department of Mathematics, Centre of Mathematics (CMAT), University of Minho, Campus de Azur\u00e9m, 4800-058, Guimar\u00e3es, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Centre of Mathematics (CMAT), University of Minho, Campus de Azur\u00e9m, 4800-058, Guimar\u00e3es, Portugal","institution_ids":["https://openalex.org/I99682543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087725371","display_name":"Neville J. Ford","orcid":"https://orcid.org/0000-0002-9446-437X"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Neville Ford","raw_affiliation_strings":["Department of Mathematics, University of Chester, Chester, CH1 4BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chester, Chester, CH1 4BJ, UK","institution_ids":["https://openalex.org/I137265193"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Maria Lu\u00edsa Morgado","orcid":null},"institutions":[{"id":"https://openalex.org/I155381812","display_name":"University of Tr\u00e1s-os-Montes and Alto Douro","ror":"https://ror.org/03qc8vh97","country_code":"PT","type":"education","lineage":["https://openalex.org/I155381812"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Maria Lu\u00edsa Morgado","raw_affiliation_strings":["Center for Computational and Stochastic Mathematics, Instituto Superior T\u00e9cnico, Universidade de Tr\u00e1s-os-Montes e Alto Douro, Departamento de Matem\u00e1tica, UTAD Quinta de Prados, 5001-801, Vila Real, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational and Stochastic Mathematics, Instituto Superior T\u00e9cnico, Universidade de Tr\u00e1s-os-Montes e Alto Douro, Departamento de Matem\u00e1tica, UTAD Quinta de Prados, 5001-801, Vila Real, Portugal","institution_ids":["https://openalex.org/I155381812"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056926916","display_name":"Magda Rebelo","orcid":"https://orcid.org/0000-0003-4115-3516"},"institutions":[{"id":"https://openalex.org/I83558840","display_name":"Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89","country_code":"PT","type":"education","lineage":["https://openalex.org/I83558840"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Magda Rebelo","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia and Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA), Universidade NOVA de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia and Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA), Universidade NOVA de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal","institution_ids":["https://openalex.org/I83558840"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I155381812"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.1582,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.52239253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"4","first_page":"535","last_page":"551"},"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":0.9970999956130981,"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":0.9966999888420105,"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":0.723021388053894},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6609135270118713},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6403628587722778},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4976702034473419},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4882412254810333},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47793319821357727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44617751240730286},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4320402443408966},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.3614917993545532}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.723021388053894},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6609135270118713},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6403628587722778},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4976702034473419},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4882412254810333},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47793319821357727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44617751240730286},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4320402443408966},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.3614917993545532}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11786-019-00448-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-019-00448-x","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/66733","is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/66733","pdf_url":null,"source":{"id":"https://openalex.org/S4306400354","display_name":"Reposit\u00f3riUM (Universidade do Minho)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99682543","host_organization_name":"University of Minho","host_organization_lineage":["https://openalex.org/I99682543"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:repositorium.uminho.pt:1822/66733","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s11786-019-00448-x","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/66733","is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/66733","pdf_url":null,"source":{"id":"https://openalex.org/S4306400354","display_name":"Reposit\u00f3riUM (Universidade do Minho)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99682543","host_organization_name":"University of Minho","host_organization_lineage":["https://openalex.org/I99682543"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W110340196","https://openalex.org/W148234565","https://openalex.org/W194858719","https://openalex.org/W617317968","https://openalex.org/W1520302938","https://openalex.org/W1528987510","https://openalex.org/W1880690653","https://openalex.org/W1963843024","https://openalex.org/W1966258563","https://openalex.org/W1966517490","https://openalex.org/W1973950856","https://openalex.org/W1975670568","https://openalex.org/W1977696410","https://openalex.org/W1982267083","https://openalex.org/W1996576314","https://openalex.org/W1998214447","https://openalex.org/W2001031344","https://openalex.org/W2008503164","https://openalex.org/W2012163408","https://openalex.org/W2020988386","https://openalex.org/W2037167871","https://openalex.org/W2038588805","https://openalex.org/W2050495940","https://openalex.org/W2056829543","https://openalex.org/W2057206818","https://openalex.org/W2063271632","https://openalex.org/W2067855936","https://openalex.org/W2088589842","https://openalex.org/W2092440717","https://openalex.org/W2092718516","https://openalex.org/W2110245394","https://openalex.org/W2116024271","https://openalex.org/W2119671522","https://openalex.org/W2142367591","https://openalex.org/W2165076033","https://openalex.org/W2167500235","https://openalex.org/W2608656286","https://openalex.org/W2757644851","https://openalex.org/W2950965409","https://openalex.org/W4247953052"],"related_works":["https://openalex.org/W2120222762","https://openalex.org/W2003948055","https://openalex.org/W2285121088","https://openalex.org/W3110316752","https://openalex.org/W2160114043","https://openalex.org/W2151471995","https://openalex.org/W2040892753","https://openalex.org/W2089857413","https://openalex.org/W2955583761","https://openalex.org/W3089647350"],"abstract_inverted_index":{"Taking":[0],"into":[1],"account":[2],"the":[3,7,24,41,45,49,66,74,79],"regularity":[4],"properties":[5],"of":[6,9,33,35,40,48,73,76],"solutions":[8,32],"fractional":[10,36],"differential":[11,38],"equations,":[12],"we":[13,53,64],"develop":[14],"a":[15,71],"numerical":[16,50,61],"method":[17,51,75],"which":[18],"is":[19],"able":[20],"to":[21],"deal,":[22],"with":[23,27],"same":[25],"accuracy,":[26],"both":[28],"smooth":[29],"and":[30,52,57,78],"nonsmooth":[31],"systems":[34],"ordinary":[37],"equations":[39],"Caputo-type.":[42],"We":[43],"provide":[44],"error":[46],"analysis":[47],"illustrate":[54],"its":[55],"feasibility":[56],"accuracy":[58],"through":[59],"some":[60],"examples.":[62],"Finally,":[63],"solve":[65],"time-fractional":[67],"diffusion":[68],"equation":[69],"using":[70],"combination":[72],"lines":[77],"newly":[80],"developed":[81],"hybrid":[82],"method.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
