{"id":"https://openalex.org/W2019324632","doi":"https://doi.org/10.1137/050642757","title":"Numerical Approximation of a Time Dependent, Nonlinear, Space\u2010Fractional Diffusion Equation","display_name":"Numerical Approximation of a Time Dependent, Nonlinear, Space\u2010Fractional Diffusion Equation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2019324632","doi":"https://doi.org/10.1137/050642757","mag":"2019324632"},"language":"en","primary_location":{"id":"doi:10.1137/050642757","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050642757","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5058872661","display_name":"Vincent J. Ervin","orcid":"https://orcid.org/0000-0003-2514-0408"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vincent J. Ervin","raw_affiliation_strings":["Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-0975, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-0975, USA","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005069559","display_name":"Norbert Heuer","orcid":"https://orcid.org/0000-0002-5171-1457"},"institutions":[{"id":"https://openalex.org/I59433898","display_name":"Brunel University of London","ror":"https://ror.org/00dn4t376","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I59433898"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Norbert Heuer","raw_affiliation_strings":["BICOM, Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK"],"affiliations":[{"raw_affiliation_string":"BICOM, Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK","institution_ids":["https://openalex.org/I59433898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054443661","display_name":"John Paul Roop","orcid":"https://orcid.org/0000-0003-4695-8946"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Paul Roop","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058872661"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":null,"apc_paid":null,"fwci":2.7342,"has_fulltext":false,"cited_by_count":245,"citation_normalized_percentile":{"value":0.88757784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"45","issue":"2","first_page":"572","last_page":"591"},"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":0.9991000294685364,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8307623863220215},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5949723720550537},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5940810441970825},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5162348747253418},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5138933658599854},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.49846959114074707},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4841199815273285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48090457916259766},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46701082587242126},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4665180444717407},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4580894708633423},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4303184747695923},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.42276760935783386},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08718037605285645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8307623863220215},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5949723720550537},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5940810441970825},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5162348747253418},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5138933658599854},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.49846959114074707},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4841199815273285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48090457916259766},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46701082587242126},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4665180444717407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4580894708633423},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4303184747695923},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.42276760935783386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08718037605285645},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050642757","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050642757","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.473.7989","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.473.7989","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.brunel.ac.uk/~icsrsss/bicom/preprint/2005/4/main.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5650521312","display_name":"Computational Analysis of Viscoelastic Fluid Flow with Applications","funder_award_id":"0410792","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338206","display_name":"Fondo de Financiamiento de Centros de Investigaci\u00f3n en \u00c1reas Prioritarias","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W560409768","https://openalex.org/W1492326914","https://openalex.org/W1553338987","https://openalex.org/W1674659126","https://openalex.org/W1966513244","https://openalex.org/W1969706981","https://openalex.org/W1983959946","https://openalex.org/W2004467399","https://openalex.org/W2004872575","https://openalex.org/W2024606917","https://openalex.org/W2051862019","https://openalex.org/W2088216803","https://openalex.org/W2113916146","https://openalex.org/W2127769310","https://openalex.org/W2988078269"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2146736923","https://openalex.org/W4213231742","https://openalex.org/W2066116605","https://openalex.org/W2011648757"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"article":[3],"we":[4],"analyze":[5],"a":[6,12,21,30,41,48,59],"fully":[7],"discrete":[8],"numerical":[9],"approximation":[10,57],"to":[11],"time":[13],"depen-dent":[14],"fractional":[15,32],"order":[16,33,52],"diffusion":[17,34],"equation":[18],"which":[19,69],"contains":[20],"non-local,":[22],"quadratic":[23],"non-linearity.":[24],"The":[25,36],"analysis":[26],"is":[27,40],"performed":[28],"for":[29],"general":[31],"operator.":[35],"non-linear":[37],"term":[38],"studied":[39],"product":[42],"of":[43,51,55],"the":[44,56,71],"unknown":[45],"function":[46],"and":[47,58],"convolution":[49],"operator":[50],"0.":[53],"Convergence":[54],"priori":[60],"error":[61],"estimates":[62],"are":[63,67],"given.":[64],"Numerical":[65],"computations":[66],"included":[68],"confirm":[70],"theoretical":[72],"predictions.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":30},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}