{"id":"https://openalex.org/W2790724496","doi":"https://doi.org/10.1080/00207160.2018.1447665","title":"A sixth-order finite difference WENO scheme for Hamilton\u2013Jacobi equations","display_name":"A sixth-order finite difference WENO scheme for Hamilton\u2013Jacobi equations","publication_year":2018,"publication_date":"2018-03-02","ids":{"openalex":"https://openalex.org/W2790724496","doi":"https://doi.org/10.1080/00207160.2018.1447665","mag":"2790724496"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2018.1447665","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1447665","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/A5066844202","display_name":"Xiaohan Cheng","orcid":"https://orcid.org/0000-0002-6324-8199"},"institutions":[{"id":"https://openalex.org/I25355098","display_name":"Chang'an University","ror":"https://ror.org/05mxya461","country_code":"CN","type":"education","lineage":["https://openalex.org/I25355098"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohan Cheng","raw_affiliation_strings":["School of Science, Chang'an University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Chang'an University, Xi'an, China","institution_ids":["https://openalex.org/I25355098"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102793036","display_name":"Jian-Hu Feng","orcid":"https://orcid.org/0000-0003-4813-043X"},"institutions":[{"id":"https://openalex.org/I25355098","display_name":"Chang'an University","ror":"https://ror.org/05mxya461","country_code":"CN","type":"education","lineage":["https://openalex.org/I25355098"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianhu Feng","raw_affiliation_strings":["School of Science, Chang'an University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Chang'an University, Xi'an, China","institution_ids":["https://openalex.org/I25355098"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066844202"],"corresponding_institution_ids":["https://openalex.org/I25355098"],"apc_list":null,"apc_paid":null,"fwci":1.0134,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72102671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"96","issue":"3","first_page":"568","last_page":"584"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987000226974487,"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":0.9984999895095825,"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/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.9027388095855713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.76552814245224},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7293375730514526},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6277987957000732},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5167750120162964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.509900689125061},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.490384578704834},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47211015224456787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4524289071559906},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.44397449493408203},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.44302356243133545},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4222768545150757},{"id":"https://openalex.org/keywords/jacobi-method","display_name":"Jacobi method","score":0.4150373041629791}],"concepts":[{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.9027388095855713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.76552814245224},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7293375730514526},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6277987957000732},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5167750120162964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.509900689125061},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.490384578704834},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47211015224456787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4524289071559906},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.44397449493408203},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.44302356243133545},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4222768545150757},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.4150373041629791},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2018.1447665","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1447665","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/G6777829708","display_name":null,"funder_award_id":"11601037 and 11401045","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1966241802","https://openalex.org/W1975738182","https://openalex.org/W1983195644","https://openalex.org/W1986838484","https://openalex.org/W2005919860","https://openalex.org/W2008295247","https://openalex.org/W2013049663","https://openalex.org/W2013714847","https://openalex.org/W2015130302","https://openalex.org/W2027438381","https://openalex.org/W2028740100","https://openalex.org/W2039802576","https://openalex.org/W2043401463","https://openalex.org/W2052454954","https://openalex.org/W2060242824","https://openalex.org/W2064852362","https://openalex.org/W2070505479","https://openalex.org/W2079578802","https://openalex.org/W2083367386","https://openalex.org/W2084413738","https://openalex.org/W2094051484","https://openalex.org/W2094141855","https://openalex.org/W2107039084","https://openalex.org/W2120290852","https://openalex.org/W2124772009","https://openalex.org/W2125671914","https://openalex.org/W2137807118","https://openalex.org/W2142699560","https://openalex.org/W2142901407","https://openalex.org/W2143454084","https://openalex.org/W2157195870","https://openalex.org/W2157204523","https://openalex.org/W2424269979","https://openalex.org/W2509790526","https://openalex.org/W2585716370","https://openalex.org/W2589271359","https://openalex.org/W2606698994","https://openalex.org/W2749408143","https://openalex.org/W4255678539"],"related_works":["https://openalex.org/W1983345526","https://openalex.org/W2076944689","https://openalex.org/W1594944678","https://openalex.org/W1977330547","https://openalex.org/W1487586009","https://openalex.org/W3102569876","https://openalex.org/W2971079383","https://openalex.org/W2061585064","https://openalex.org/W575199273","https://openalex.org/W2022926609"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"sixth-order":[4,63],"finite":[5],"difference":[6],"weighted":[7],"essentially":[8],"non-oscillatory":[9],"(WENO)":[10],"scheme":[11,26,37],"is":[12],"developed":[13],"to":[14,90],"approximate":[15],"the":[16,20,28,33,92,95],"viscosity":[17],"solution":[18],"of":[19,94],"Hamilton\u2013Jacobi":[21,47],"equations.":[22],"This":[23],"new":[24],"WENO":[25,36],"has":[27],"same":[29],"spatial":[30],"nodes":[31],"as":[32,60,62],"classical":[34],"fifth-order":[35],"proposed":[38,96],"by":[39],"Jiang":[40],"and":[41,84],"Peng":[42],"[Weighted":[43],"ENO":[44],"schemes":[45],"for":[46],"equations,":[48],"SIAM.":[49],"J.":[50],"Sci.":[51],"Comput.":[52],"21":[53],"(2000),":[54],"pp.":[55],"2126\u20132143]":[56],"but":[57],"can":[58],"be":[59],"high":[61],"accurate":[64],"in":[65,82],"smooth":[66],"region":[67],"while":[68],"keeping":[69],"sharp":[70],"discontinuous":[71],"transitions":[72],"with":[73],"no":[74],"spurious":[75],"oscillations":[76],"near":[77],"discontinuities.":[78],"Extensive":[79],"numerical":[80],"experiments":[81],"one-":[83],"two-dimensional":[85],"cases":[86],"are":[87],"carried":[88],"out":[89],"illustrate":[91],"capability":[93],"scheme.":[97]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
