{"id":"https://openalex.org/W2083790997","doi":"https://doi.org/10.1155/2012/308410","title":"Numerical Analysis of a Linear\u2010Implicit Average Scheme for Generalized Benjamin\u2010Bona\u2010Mahony\u2010Burgers Equation","display_name":"Numerical Analysis of a Linear\u2010Implicit Average Scheme for Generalized Benjamin\u2010Bona\u2010Mahony\u2010Burgers Equation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2083790997","doi":"https://doi.org/10.1155/2012/308410","mag":"2083790997"},"language":"en","primary_location":{"id":"doi:10.1155/2012/308410","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/308410","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/308410.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/308410.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024748893","display_name":"Haitao Che","orcid":"https://orcid.org/0000-0002-4632-0603"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]},{"id":"https://openalex.org/I66883779","display_name":"Weifang University","ror":"https://ror.org/01frp7483","country_code":"CN","type":"education","lineage":["https://openalex.org/I66883779"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hai-tao Che","raw_affiliation_strings":["School of Management Science, Qufu Normal University, Rizhao 276800","School of Mathematics and Information Science, Weifang University, Weifang 261061"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management Science, Qufu Normal University, Rizhao 276800","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Weifang University, Weifang 261061","institution_ids":["https://openalex.org/I66883779"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084428311","display_name":"Xintian Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I66883779","display_name":"Weifang University","ror":"https://ror.org/01frp7483","country_code":"CN","type":"education","lineage":["https://openalex.org/I66883779"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin-tian Pan","raw_affiliation_strings":["School of Mathematics and Information Science, Weifang University, Weifang 261061"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Weifang University, Weifang 261061","institution_ids":["https://openalex.org/I66883779"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111855192","display_name":"Luming Zhang","orcid":"https://orcid.org/0009-0007-0596-3294"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu-ming Zhang","raw_affiliation_strings":["Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103281173","display_name":"Yiju Wang","orcid":"https://orcid.org/0000-0003-4802-2172"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi-ju Wang","raw_affiliation_strings":["School of Management Science, Qufu Normal University, Rizhao 276800"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management Science, Qufu Normal University, Rizhao 276800","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024748893"],"corresponding_institution_ids":["https://openalex.org/I202126657","https://openalex.org/I66883779"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.2427,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.57246756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9958999752998352,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9944999814033508,"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":0.8418022394180298},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6361063122749329},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.616744875907898},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.6083041429519653},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5585915446281433},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5158213973045349},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5084139704704285},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4615353047847748},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45195430517196655},{"id":"https://openalex.org/keywords/energy-method","display_name":"Energy method","score":0.43840548396110535},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4103318750858307},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.23504719138145447}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8418022394180298},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6361063122749329},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.616744875907898},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.6083041429519653},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5585915446281433},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5158213973045349},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5084139704704285},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4615353047847748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45195430517196655},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.43840548396110535},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4103318750858307},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.23504719138145447},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/308410","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/308410","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/308410.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495065","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495065","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:308410","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/308410.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:ee089c4d2d7546d6ac5bad3869c884fa","is_oa":true,"landing_page_url":"https://doaj.org/article/ee089c4d2d7546d6ac5bad3869c884fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/308410","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/308410","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/308410.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.7799999713897705}],"awards":[{"id":"https://openalex.org/G2802426757","display_name":null,"funder_award_id":"2011Z17","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2853807951","display_name":null,"funder_award_id":"11171193","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"},{"id":"https://openalex.org/G364944359","display_name":null,"funder_award_id":"ZR2009AL019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4510131305","display_name":null,"funder_award_id":"ZR2011AM016","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"},{"id":"https://openalex.org/G5296216040","display_name":null,"funder_award_id":"ZR2009AL019","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"},{"id":"https://openalex.org/G5300459596","display_name":null,"funder_award_id":"2011Z17","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"},{"id":"https://openalex.org/G5410887993","display_name":null,"funder_award_id":"11171180","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6195672269","display_name":"\u589e\u5e7f\u62c9\u683c\u6717\u65e5\u95ee\u9898\u7684\u5e94\u7528\u7814\u7a76","funder_award_id":"10901096","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7349512832","display_name":null,"funder_award_id":"11171193","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7774568775","display_name":null,"funder_award_id":"11171180","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"},{"id":"https://openalex.org/G8305705803","display_name":null,"funder_award_id":"ZR2011AM016","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8618077386","display_name":null,"funder_award_id":"10901096","funder_id":"https://openalex.org/F4320309558","funder_display_name":"Wake Forest University"}],"funders":[{"id":"https://openalex.org/F4320309558","display_name":"Wake Forest University","ror":"https://ror.org/0207ad724"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2083790997.pdf","grobid_xml":"https://content.openalex.org/works/W2083790997.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1964990804","https://openalex.org/W1967060665","https://openalex.org/W1972142662","https://openalex.org/W1977070309","https://openalex.org/W1994377097","https://openalex.org/W2005380085","https://openalex.org/W2014292079","https://openalex.org/W2027557504","https://openalex.org/W2028619832","https://openalex.org/W2029469957","https://openalex.org/W2043754866","https://openalex.org/W2061389942","https://openalex.org/W2070084642","https://openalex.org/W2076446243","https://openalex.org/W2077068703","https://openalex.org/W2077464783","https://openalex.org/W2078773005","https://openalex.org/W2088006179","https://openalex.org/W2132775908","https://openalex.org/W2185749334","https://openalex.org/W2764433274","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2615167981","https://openalex.org/W4388311650","https://openalex.org/W2033424684","https://openalex.org/W2075198862","https://openalex.org/W2385894824","https://openalex.org/W2263717523","https://openalex.org/W2124159608","https://openalex.org/W2049416585","https://openalex.org/W2034966818","https://openalex.org/W2318783616"],"abstract_inverted_index":{"A":[0,28],"linear\u2010implicit":[1],"finite":[2,36],"difference":[3,37],"scheme":[4,50],"is":[5,15,26,51],"given":[6],"for":[7],"the":[8,35,49],"initial\u2010boundary":[9],"problem":[10],"of":[11,23,34],"GBBM\u2010Burgers":[12],"equation,":[13],"which":[14],"convergent":[16],"and":[17,31,53],"unconditionally":[18],"stable.":[19],"The":[20],"unique":[21],"solvability":[22],"numerical":[24],"solutions":[25],"shown.":[27],"priori":[29],"estimate":[30],"second\u2010order":[32],"convergence":[33],"approximate":[38],"solution":[39],"are":[40],"discussed":[41],"using":[42],"energy":[43],"method.":[44],"Numerical":[45],"results":[46],"demonstrate":[47],"that":[48],"efficient":[52],"accurate.":[54]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2016-06-24T00:00:00"}