{"id":"https://openalex.org/W1981090966","doi":"https://doi.org/10.1155/2014/597926","title":"Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations","display_name":"Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1981090966","doi":"https://doi.org/10.1155/2014/597926","mag":"1981090966"},"language":"en","primary_location":{"id":"doi:10.1155/2014/597926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/597926","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/597926.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/2014/597926.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101763650","display_name":"Lei Zhang","orcid":"https://orcid.org/0000-0003-2513-0656"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100770516","display_name":"Lisha Wang","orcid":"https://orcid.org/0000-0002-6482-1073"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lisha Wang","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101413900","display_name":"Xiaohua Ding","orcid":"https://orcid.org/0000-0002-0983-3522"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohua Ding","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101413900"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":0.8659,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.71904734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9983999729156494,"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":0.9983999729156494,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9976000189781189,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.8964766263961792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8189720511436462},{"id":"https://openalex.org/keywords/fisher-equation","display_name":"Fisher equation","score":0.5890705585479736},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5607231855392456},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5290930271148682},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.5165508985519409},{"id":"https://openalex.org/keywords/fishers-equation","display_name":"Fisher's equation","score":0.5068560242652893},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4900909662246704},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4370800256729126},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4341360926628113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4261387586593628},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.36641305685043335},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.28060540556907654},{"id":"https://openalex.org/keywords/method-of-characteristics","display_name":"Method of characteristics","score":0.1283351182937622}],"concepts":[{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.8964766263961792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8189720511436462},{"id":"https://openalex.org/C61031149","wikidata":"https://www.wikidata.org/wiki/Q1153200","display_name":"Fisher equation","level":4,"score":0.5890705585479736},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5607231855392456},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5290930271148682},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.5165508985519409},{"id":"https://openalex.org/C48170192","wikidata":"https://www.wikidata.org/wiki/Q1763840","display_name":"Fisher's equation","level":5,"score":0.5068560242652893},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4900909662246704},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4370800256729126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4341360926628113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4261387586593628},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.36641305685043335},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.28060540556907654},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.1283351182937622},{"id":"https://openalex.org/C175025494","wikidata":"https://www.wikidata.org/wiki/Q179179","display_name":"Interest rate","level":2,"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/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.0},{"id":"https://openalex.org/C154815372","wikidata":"https://www.wikidata.org/wiki/Q1140421","display_name":"Real interest rate","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/597926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/597926","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/597926.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/1395855271","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1395855271","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:597926","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/597926.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:37743151f7264e189211f9078f7b776a","is_oa":true,"landing_page_url":"https://doaj.org/article/37743151f7264e189211f9078f7b776a","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 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/597926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/597926","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/597926.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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":[],"awards":[{"id":"https://openalex.org/G1622615635","display_name":null,"funder_award_id":"ZR2010AQ021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2104725390","display_name":null,"funder_award_id":"HIT.NSRIF.2011104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G386922295","display_name":null,"funder_award_id":"ZR2010AQ021","funder_id":"https://openalex.org/F4320321940","funder_display_name":"Harbin Institute of Technology"},{"id":"https://openalex.org/G590693389","display_name":null,"funder_award_id":"ZR2010AQ021","funder_id":"https://openalex.org/F4320327935","funder_display_name":"Weihai Science and Technology Development Program"},{"id":"https://openalex.org/G5929459947","display_name":null,"funder_award_id":"2010-3-96","funder_id":"https://openalex.org/F4320321940","funder_display_name":"Harbin Institute of Technology"},{"id":"https://openalex.org/G6879051387","display_name":null,"funder_award_id":"2010-3-96","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7933713859","display_name":null,"funder_award_id":"11026189","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321940","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08"},{"id":"https://openalex.org/F4320327935","display_name":"Weihai Science and Technology Development Program","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1981090966.pdf","grobid_xml":"https://content.openalex.org/works/W1981090966.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W396155428","https://openalex.org/W603207913","https://openalex.org/W648809531","https://openalex.org/W1967088341","https://openalex.org/W1970793397","https://openalex.org/W1971498077","https://openalex.org/W1973385986","https://openalex.org/W1979708666","https://openalex.org/W1980128768","https://openalex.org/W1981554056","https://openalex.org/W1984960976","https://openalex.org/W1986788497","https://openalex.org/W1988159463","https://openalex.org/W1994977368","https://openalex.org/W2001501290","https://openalex.org/W2004320578","https://openalex.org/W2009153306","https://openalex.org/W2032143293","https://openalex.org/W2032919599","https://openalex.org/W2037533572","https://openalex.org/W2041108583","https://openalex.org/W2072717011","https://openalex.org/W2074083049","https://openalex.org/W2079929209","https://openalex.org/W2085425687","https://openalex.org/W2094402315","https://openalex.org/W2317065091","https://openalex.org/W2329115484","https://openalex.org/W2964266188","https://openalex.org/W4231712415","https://openalex.org/W4251682376","https://openalex.org/W4254425416","https://openalex.org/W4300489453"],"related_works":["https://openalex.org/W2522176984","https://openalex.org/W4386298212","https://openalex.org/W2348758072","https://openalex.org/W2359484516","https://openalex.org/W2001753714","https://openalex.org/W2903479806","https://openalex.org/W2053580463","https://openalex.org/W2050702845","https://openalex.org/W2616033000","https://openalex.org/W1981090966"],"abstract_inverted_index":{"We":[0],"present":[1],"finite":[2,16,34],"difference":[3,17,35],"schemes":[4,36],"for":[5,19],"Burgers":[6,20],"equation":[7,21,24],"and":[8,22,51],"Burgers-Fisher":[9,23],"equation.":[10],"A":[11],"new":[12],"version":[13],"of":[14,53],"exact":[15],"scheme":[18],"is":[25],"proposed":[26],"using":[27],"the":[28,49],"solitary":[29],"wave":[30],"solution.":[31],"Then":[32],"nonstandard":[33],"are":[37,45],"constructed":[38],"to":[39,47],"solve":[40],"two":[41],"equations.":[42],"Numerical":[43],"experiments":[44],"presented":[46],"verify":[48],"accuracy":[50],"efficiency":[52],"such":[54],"NSFD":[55],"schemes.":[56]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}