{"id":"https://openalex.org/W4396771827","doi":"https://doi.org/10.1080/00207160.2024.2351132","title":"A BDF2 method for a singularly perturbed transport equation","display_name":"A BDF2 method for a singularly perturbed transport equation","publication_year":2024,"publication_date":"2024-05-03","ids":{"openalex":"https://openalex.org/W4396771827","doi":"https://doi.org/10.1080/00207160.2024.2351132"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2024.2351132","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2024.2351132","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/A5003721958","display_name":"Zhongdi Cen","orcid":"https://orcid.org/0000-0001-9739-2036"},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongdi Cen","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, People\u2019s Republic of China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, People\u2019s Republic of China","institution_ids":["https://openalex.org/I1315279114"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, People's Republic of China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100523812","display_name":"Aimin Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aimin Xu","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, People\u2019s Republic of China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, People\u2019s Republic of China","institution_ids":["https://openalex.org/I1315279114"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, People's Republic of China","institution_ids":["https://openalex.org/I1315279114"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003721958"],"corresponding_institution_ids":["https://openalex.org/I1315279114"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10474951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"101","issue":"5","first_page":"538","last_page":"548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9593999981880188,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9574000239372253,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.4593413770198822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44529515504837036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4377768039703369},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4112769067287445},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34173911809921265},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.33186787366867065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2560758590698242}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4593413770198822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44529515504837036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4377768039703369},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4112769067287445},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34173911809921265},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.33186787366867065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2560758590698242}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2024.2351132","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2024.2351132","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/G352511639","display_name":null,"funder_award_id":"2023J203","funder_id":"https://openalex.org/F4320323225","funder_display_name":"Natural Science Foundation of Ningbo Municipality"}],"funders":[{"id":"https://openalex.org/F4320323225","display_name":"Natural Science Foundation of Ningbo Municipality","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1973297078","https://openalex.org/W2769217581","https://openalex.org/W2912456117","https://openalex.org/W3046790868","https://openalex.org/W3151605865","https://openalex.org/W3186719682","https://openalex.org/W4238363765","https://openalex.org/W4293151546","https://openalex.org/W4312224081","https://openalex.org/W4384206493"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"A":[0,7],"singularly":[1,27],"perturbed":[2,28],"transport":[3,29],"equation":[4],"is":[5,18,46,51],"considered.":[6],"variable":[8],"two-step":[9],"backward":[10],"differentiation":[11],"formulas":[12],"(BDF2)":[13],"on":[14],"a":[15],"Shishkin-type":[16],"mesh":[17],"used":[19],"to":[20,57,69],"discrete":[21,41],"the":[22,26,40,49,58,71],"first-order":[23],"derivatives":[24],"of":[25],"equation.":[30],"The":[31],"stability":[32],"and":[33],"error":[34],"analysis":[35],"are":[36,67],"derived":[37],"by":[38],"using":[39],"orthogonal":[42],"convolution":[43],"kernels.":[44],"It":[45],"proved":[47],"that":[48],"scheme":[50],"second-order":[52],"uniformly":[53],"convergent":[54],"with":[55],"respect":[56],"small":[59],"parameter,":[60],"which":[61],"improves":[62],"previous":[63],"results.":[64],"Numerical":[65],"experiments":[66],"presented":[68],"support":[70],"theoretical":[72],"result.":[73]},"counts_by_year":[],"updated_date":"2025-12-21T23:12:01.093139","created_date":"2025-10-10T00:00:00"}