{"id":"https://openalex.org/W4312354951","doi":"https://doi.org/10.3934/nhm.2023014","title":"The numerical solutions for the nonhomogeneous Burgers' equation with the generalized Hopf-Cole transformation","display_name":"The numerical solutions for the nonhomogeneous Burgers' equation with the generalized Hopf-Cole transformation","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312354951","doi":"https://doi.org/10.3934/nhm.2023014"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2023014","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023014","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2023014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007179533","display_name":"Tong Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tong Yan","raw_affiliation_strings":["Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China","institution_ids":["https://openalex.org/I1328775524"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007179533"],"corresponding_institution_ids":["https://openalex.org/I1328775524"],"apc_list":null,"apc_paid":null,"fwci":0.2706,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50174333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"18","issue":"1","first_page":"359","last_page":"379"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9991000294685364,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965000152587891,"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":0.7742446660995483},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.7060285210609436},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5221638679504395},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5214223861694336},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5129261016845703},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4888979494571686},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4749320149421692},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46598878502845764},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.46386995911598206},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45744699239730835},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4570910334587097},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.20353665947914124}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742446660995483},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.7060285210609436},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5221638679504395},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5214223861694336},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5129261016845703},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4888979494571686},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4749320149421692},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46598878502845764},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.46386995911598206},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45744699239730835},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4570910334587097},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.20353665947914124},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2023014","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023014","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:aae680443d94463384772e2c12b07679","is_oa":true,"landing_page_url":"https://doaj.org/article/aae680443d94463384772e2c12b07679","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 18, Iss 1, Pp 359-379 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2023014","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023014","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8799999952316284,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1057021034","https://openalex.org/W1972860094","https://openalex.org/W1988695560","https://openalex.org/W1989188636","https://openalex.org/W2000990426","https://openalex.org/W2014283195","https://openalex.org/W2025077665","https://openalex.org/W2042386123","https://openalex.org/W2045384647","https://openalex.org/W2076823706","https://openalex.org/W2092586942","https://openalex.org/W2095179029","https://openalex.org/W2561980341","https://openalex.org/W2565432921","https://openalex.org/W2606175111","https://openalex.org/W2801242492","https://openalex.org/W2943867078","https://openalex.org/W3011992214","https://openalex.org/W3034202664","https://openalex.org/W3038217604","https://openalex.org/W3042789352","https://openalex.org/W3121746194","https://openalex.org/W3138360472"],"related_works":["https://openalex.org/W1990592929","https://openalex.org/W2030290168","https://openalex.org/W2567323499","https://openalex.org/W2266389965","https://openalex.org/W2490803538","https://openalex.org/W2368213093","https://openalex.org/W2888445389","https://openalex.org/W4294229679","https://openalex.org/W1967943375","https://openalex.org/W3155317464"],"abstract_inverted_index":{"&lt;abstract&gt;&lt;p&gt;In":[0],"this":[1,73],"paper,":[2],"with":[3,23],"the":[4,7,14,24,50,58,77,84,88,92,96,104,116],"help":[5],"of":[6,87],"generalized":[8],"Hopf-Cole":[9],"transformation,":[10],"we":[11,67,82],"first":[12],"convert":[13,57],"nonhomogeneous":[15,129],"Burgers'":[16,130],"equation":[17,22],"into":[18,60],"an":[19,61],"equivalent":[20,62],"heat":[21],"derivative":[25],"boundary":[26,31,35],"conditions,":[27],"in":[28],"which":[29,114],"Neumann":[30],"conditions":[32,36],"and":[33,47,98,128],"Robin":[34],"can":[37,120],"be":[38],"viewed":[39],"as":[40],"its":[41],"special":[42],"cases.":[43],"For":[44],"easy":[45],"derivation":[46],"numerical":[48,89,109],"analysis,":[49],"reduction":[51],"order":[52],"method":[53],"is":[54],"used":[55],"to":[56],"problem":[59],"first-order":[63,74],"coupled":[64],"system.":[65,75],"Next,":[66],"establish":[68],"a":[69],"box":[70,93,118],"scheme":[71,119],"for":[72,91,125],"By":[76],"technical":[78],"energy":[79],"analysis":[80],"method,":[81],"obtain":[83],"prior":[85,105],"estimate":[86],"solution":[90],"scheme.":[94],"Furthermore,":[95],"solvability":[97],"convergence":[99],"are":[100,111],"obtained":[101],"directly":[102],"from":[103],"estimate.":[106],"The":[107],"extensive":[108],"examples":[110],"carried":[112],"out,":[113],"verify":[115],"developed":[117],"achieve":[121],"global":[122],"second-order":[123],"accuracy":[124],"both":[126],"homogeneous":[127],"equations.&lt;/p&gt;&lt;/abstract&gt;":[131]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
