{"id":"https://openalex.org/W2798189136","doi":"https://doi.org/10.1515/cmam-2018-0002","title":"The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation","display_name":"The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation","publication_year":2018,"publication_date":"2018-03-03","ids":{"openalex":"https://openalex.org/W2798189136","doi":"https://doi.org/10.1515/cmam-2018-0002","mag":"2798189136"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0002","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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/A5009476835","display_name":"\u0412. \u041b. \u041c\u0430\u043a\u0430\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0002-4883-6574"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Volodymyr Makarov","raw_affiliation_strings":["Department of Numerical Mathematics , Institute of Mathematics of the National Academy of Sciences of Ukraine , 3 Tereshchenkivska Str., 01004 Kyiv , Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-4883-6574","affiliations":[{"raw_affiliation_string":"Department of Numerical Mathematics , Institute of Mathematics of the National Academy of Sciences of Ukraine , 3 Tereshchenkivska Str., 01004 Kyiv , Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050301139","display_name":"N. V. Mayko","orcid":"https://orcid.org/0000-0002-8810-7464"},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Nataliya Mayko","raw_affiliation_strings":["Faculty of Radiophysics, Electronics and Computer Systems , Department of Mathematics and Theoretical Radiophysics , Taras Shevchenko National University of Kyiv , 64/13 Volodymyrska Str., 01601 Kyiv , Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-8810-7464","affiliations":[{"raw_affiliation_string":"Faculty of Radiophysics, Electronics and Computer Systems , Department of Mathematics and Theoretical Radiophysics , Taras Shevchenko National University of Kyiv , 64/13 Volodymyrska Str., 01601 Kyiv , Ukraine","institution_ids":["https://openalex.org/I189238007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050301139"],"corresponding_institution_ids":["https://openalex.org/I189238007"],"apc_list":null,"apc_paid":null,"fwci":0.9338,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72994095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"19","issue":"2","first_page":"379","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9993000030517578,"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":0.998199999332428,"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":0.7751307487487793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6441630125045776},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.5885581970214844},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.5873304605484009},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5695688128471375},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5165299773216248},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5004997253417969},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4933702051639557},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4895128011703491},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.48825812339782715},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4505121409893036},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.4478526711463928},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4312356412410736},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.42415574193000793},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.410695344209671},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32897600531578064},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.26491251587867737},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17261186242103577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06696754693984985}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7751307487487793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6441630125045776},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.5885581970214844},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.5873304605484009},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5695688128471375},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5165299773216248},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5004997253417969},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4933702051639557},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4895128011703491},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.48825812339782715},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4505121409893036},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4478526711463928},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4312356412410736},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.42415574193000793},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.410695344209671},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32897600531578064},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.26491251587867737},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17261186242103577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06696754693984985},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0002","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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":18,"referenced_works":["https://openalex.org/W85426232","https://openalex.org/W385499458","https://openalex.org/W1447624187","https://openalex.org/W1530054495","https://openalex.org/W1552429594","https://openalex.org/W1976424989","https://openalex.org/W2023767060","https://openalex.org/W2026904232","https://openalex.org/W2065232540","https://openalex.org/W2071593170","https://openalex.org/W2116670613","https://openalex.org/W2359912437","https://openalex.org/W2521106538","https://openalex.org/W2581135070","https://openalex.org/W2751029794","https://openalex.org/W3113221786","https://openalex.org/W4205604664","https://openalex.org/W6600500328"],"related_works":["https://openalex.org/W4299860049","https://openalex.org/W2963644996","https://openalex.org/W2745056778","https://openalex.org/W1737185509","https://openalex.org/W815539758","https://openalex.org/W2804722144","https://openalex.org/W3155098563","https://openalex.org/W2767841216","https://openalex.org/W2800369554","https://openalex.org/W2029595409"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"grid":[2,76],"method":[3,77],"for":[4,11],"solving":[5],"the":[6,18,32,37,44,49,52,61,65,71,75,81,84,90,94],"first":[7],"boundary":[8,46,82],"value":[9],"problem":[10],"ordinary":[12],"and":[13,36,57],"partial":[14],"differential":[15],"equations":[16],"with":[17],"Riemann\u2013Liouville":[19],"fractional":[20],"derivative":[21],"is":[22,26,55,78,88],"justified.":[23],"The":[24,41],"algorithm":[25],"based":[27],"on":[28,48],"using":[29],"Green\u2019s":[30],"function,":[31],"Fredholm":[33],"integral":[34],"equation,":[35],"Lagrange":[38],"interpolation":[39],"polynomial.":[40],"impact":[42],"of":[43,51,74,83,93],"Dirichlet":[45],"condition":[47],"accuracy":[50,72],"approximate":[53],"solution":[54],"revealed":[56],"quantitatively":[58],"described":[59],"through":[60],"weight":[62],"assessment.":[63],"All":[64],"estimates":[66],"provide":[67],"clear":[68],"evidence":[69],"that":[70],"order":[73],"higher":[79],"near":[80],"domain":[85],"than":[86],"it":[87],"in":[89],"inner":[91],"nodes":[92],"mesh":[95],"set.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}