{"id":"https://openalex.org/W2766854994","doi":"https://doi.org/10.1080/00207160.2017.1398322","title":"A high-order numerical scheme for the impulsive fractional ordinary differential equations","display_name":"A high-order numerical scheme for the impulsive fractional ordinary differential equations","publication_year":2017,"publication_date":"2017-10-31","ids":{"openalex":"https://openalex.org/W2766854994","doi":"https://doi.org/10.1080/00207160.2017.1398322","mag":"2766854994"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1398322","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1398322","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/A5074022886","display_name":"Junying Cao","orcid":"https://orcid.org/0000-0003-2246-0967"},"institutions":[{"id":"https://openalex.org/I4210095439","display_name":"Guizhou Minzu University","ror":"https://ror.org/00qm4t918","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210095439"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junying Cao","raw_affiliation_strings":["School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, China"],"affiliations":[{"raw_affiliation_string":"School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, China","institution_ids":["https://openalex.org/I4210095439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100646528","display_name":"Lizhen Chen","orcid":"https://orcid.org/0000-0001-7201-9956"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lizhen Chen","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100400479","display_name":"Ziqiang Wang","orcid":"https://orcid.org/0000-0002-6883-8569"},"institutions":[{"id":"https://openalex.org/I4210095439","display_name":"Guizhou Minzu University","ror":"https://ror.org/00qm4t918","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210095439"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ziqiang Wang","raw_affiliation_strings":["School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, China"],"affiliations":[{"raw_affiliation_string":"School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, China","institution_ids":["https://openalex.org/I4210095439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100400479"],"corresponding_institution_ids":["https://openalex.org/I4210095439"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.13402636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"95","issue":"12","first_page":"2433","last_page":"2457"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8344453573226929},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6462986469268799},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6316078305244446},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5920075178146362},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5457214713096619},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4936715066432953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47291287779808044},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4718204438686371},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4570621848106384},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.4410867989063263},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.43578052520751953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4221070408821106},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4200579524040222},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4114436209201813},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11080482602119446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09630230069160461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8344453573226929},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6462986469268799},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6316078305244446},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5920075178146362},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5457214713096619},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4936715066432953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47291287779808044},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4718204438686371},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4570621848106384},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.4410867989063263},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.43578052520751953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4221070408821106},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4200579524040222},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4114436209201813},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11080482602119446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09630230069160461},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/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:10.1080/00207160.2017.1398322","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1398322","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/G2076263841","display_name":null,"funder_award_id":"[2014]2098","funder_id":"https://openalex.org/F4320322272","funder_display_name":"Guizhou Science and Technology Department"},{"id":"https://openalex.org/G4363432893","display_name":null,"funder_award_id":"11501140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5405721928","display_name":null,"funder_award_id":"U1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G546657051","display_name":null,"funder_award_id":"11671166","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6276505845","display_name":null,"funder_award_id":"2015M580038","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7529985399","display_name":null,"funder_award_id":"[2017]1086","funder_id":"https://openalex.org/F4320322272","funder_display_name":"Guizhou Science and Technology 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/F4320322272","display_name":"Guizhou Science and Technology Department","ror":"https://ror.org/00kwnh405"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W566434069","https://openalex.org/W602720839","https://openalex.org/W1938621654","https://openalex.org/W1970546830","https://openalex.org/W1981384091","https://openalex.org/W2001038086","https://openalex.org/W2009104707","https://openalex.org/W2013471107","https://openalex.org/W2045953892","https://openalex.org/W2050240106","https://openalex.org/W2062266804","https://openalex.org/W2069936968","https://openalex.org/W2069953772","https://openalex.org/W2079408866","https://openalex.org/W2085534818","https://openalex.org/W2091845113","https://openalex.org/W2139227432","https://openalex.org/W2179638649","https://openalex.org/W2319089385","https://openalex.org/W2611201473","https://openalex.org/W2787959293","https://openalex.org/W2793444638"],"related_works":["https://openalex.org/W2102789413","https://openalex.org/W2096467061","https://openalex.org/W1532287630","https://openalex.org/W2940603871","https://openalex.org/W2052500721","https://openalex.org/W2082296130","https://openalex.org/W4299508867","https://openalex.org/W2553664144","https://openalex.org/W2913782054","https://openalex.org/W2056289616"],"abstract_inverted_index":{"In":[0,40],"this":[1],"paper,":[2],"we":[3],"use":[4],"a":[5,10,33],"good":[6],"technique":[7,23],"to":[8,51,93,118],"construct":[9],"high-order":[11],"numerical":[12,90,114],"scheme":[13,83],"for":[14,36,100],"the":[15,27,37,43,53,56,67,82,89,94,105,108,120],"impulsive":[16],"fractional":[17,109],"ordinary":[18],"differential":[19],"equations":[20],"(IFODEs).":[21],"This":[22],"is":[24,32,47,104],"based":[25],"on":[26],"so-called":[28],"block-by-block":[29,45],"method,":[30],"which":[31],"common":[34],"method":[35,46],"integral":[38],"equations.":[39],"our":[41],"approach,":[42],"classical":[44],"improved":[48],"so":[49],"as":[50],"avoid":[52],"coupling":[54],"of":[55,81,107,113],"unknown":[57],"solutions":[58],"at":[59],"each":[60],"block":[61],"step":[62],"with":[63,97],"an":[64],"exception":[65],"in":[66],"first":[68],"two":[69,72],"steps":[70],"between":[71],"adjacent":[73],"pulse":[74],"points.":[75],"The":[76],"convergence":[77],"and":[78],"stability":[79],"analysis":[80],"are":[84,116],"given.":[85],"It":[86],"proves":[87],"that":[88],"solution":[91,96],"converges":[92],"exact":[95],"order":[98,106],"3+q":[99],"0<q\u22641,":[101],"where":[102],"q":[103],"derivative.":[110],"A":[111],"series":[112],"examples":[115],"provided":[117],"support":[119],"theoretical":[121],"results.":[122]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
