{"id":"https://openalex.org/W4214952120","doi":"https://doi.org/10.3390/axioms11030111","title":"High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations","display_name":"High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations","publication_year":2022,"publication_date":"2022-03-03","ids":{"openalex":"https://openalex.org/W4214952120","doi":"https://doi.org/10.3390/axioms11030111"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11030111","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030111","pdf_url":"https://www.mdpi.com/2075-1680/11/3/111/pdf?version=1646379745","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/3/111/pdf?version=1646379745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jianying Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianying Wei","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100754640","display_name":"Yongbin Ge","orcid":"https://orcid.org/0000-0002-4071-1937"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongbin Ge","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China"],"raw_orcid":"https://orcid.org/0000-0002-4071-1937","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101920776","display_name":"Yan Wang","orcid":"https://orcid.org/0000-0003-3943-3594"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I21642278"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100754640"],"corresponding_institution_ids":["https://openalex.org/I21642278"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.2809,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74179324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"3","first_page":"111","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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":1.0,"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/T11416","display_name":"Numerical methods for differential equations","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":0.9998000264167786,"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/stencil","display_name":"Stencil","score":0.9253027439117432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887473464012146},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6801124811172485},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.6455448865890503},{"id":"https://openalex.org/keywords/von-neumann-stability-analysis","display_name":"Von Neumann stability analysis","score":0.618735671043396},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5396776795387268},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5031248927116394},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.49446606636047363},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4916098713874817},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.48401471972465515},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.47191646695137024},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4470609128475189},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.439200222492218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42402416467666626},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41478797793388367},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.39198651909828186},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.3634158670902252},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1742691695690155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13626500964164734},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07462611794471741}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.9253027439117432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887473464012146},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6801124811172485},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.6455448865890503},{"id":"https://openalex.org/C71477052","wikidata":"https://www.wikidata.org/wiki/Q458556","display_name":"Von Neumann stability analysis","level":4,"score":0.618735671043396},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5396776795387268},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5031248927116394},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.49446606636047363},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4916098713874817},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.48401471972465515},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.47191646695137024},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4470609128475189},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.439200222492218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42402416467666626},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41478797793388367},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.39198651909828186},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3634158670902252},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1742691695690155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13626500964164734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07462611794471741},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11030111","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030111","pdf_url":"https://www.mdpi.com/2075-1680/11/3/111/pdf?version=1646379745","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:447007a6bed74b6baa840286e58b1f05","is_oa":true,"landing_page_url":"https://doaj.org/article/447007a6bed74b6baa840286e58b1f05","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":"Axioms, Vol 11, Iss 3, p 111 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/3/111/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11030111","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 3; Pages: 111","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11030111","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030111","pdf_url":"https://www.mdpi.com/2075-1680/11/3/111/pdf?version=1646379745","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1232573025","display_name":null,"funder_award_id":"11902170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2080937049","display_name":null,"funder_award_id":"2018BEE03007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G307924310","display_name":null,"funder_award_id":"12161067","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4024470319","display_name":null,"funder_award_id":"2161067, 11961054, 11902170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4397907366","display_name":null,"funder_award_id":"11961054","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4722115352","display_name":null,"funder_award_id":"11961054","funder_id":"https://openalex.org/F4320334010","funder_display_name":"Key Research and Development Program of Ningxia"},{"id":"https://openalex.org/G4773438052","display_name":null,"funder_award_id":"2018BEE03007","funder_id":"https://openalex.org/F4320334010","funder_display_name":"Key Research and Development Program of Ningxia"},{"id":"https://openalex.org/G5156298376","display_name":null,"funder_award_id":"12161067","funder_id":"https://openalex.org/F4320334010","funder_display_name":"Key Research and Development Program of Ningxia"},{"id":"https://openalex.org/G7398628767","display_name":null,"funder_award_id":"11902170","funder_id":"https://openalex.org/F4320334010","funder_display_name":"Key Research and Development Program of Ningxia"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334010","display_name":"Key Research and Development Program of Ningxia","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4214952120.pdf","grobid_xml":"https://content.openalex.org/works/W4214952120.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1982117438","https://openalex.org/W1982500459","https://openalex.org/W1996996069","https://openalex.org/W2000990426","https://openalex.org/W2013106503","https://openalex.org/W2015301863","https://openalex.org/W2015391089","https://openalex.org/W2015923132","https://openalex.org/W2026621117","https://openalex.org/W2031753742","https://openalex.org/W2034598676","https://openalex.org/W2043619299","https://openalex.org/W2059138579","https://openalex.org/W2060187899","https://openalex.org/W2092333333","https://openalex.org/W2093842327","https://openalex.org/W2103606462","https://openalex.org/W2109351597","https://openalex.org/W2118085053","https://openalex.org/W2125529818","https://openalex.org/W2143720623","https://openalex.org/W2145961615","https://openalex.org/W2150511304","https://openalex.org/W2160642865","https://openalex.org/W2185007447","https://openalex.org/W2288540620","https://openalex.org/W2466437110","https://openalex.org/W2700243587","https://openalex.org/W2737417353","https://openalex.org/W2783426371","https://openalex.org/W2814342635","https://openalex.org/W2896099360","https://openalex.org/W2897319337","https://openalex.org/W2897528626","https://openalex.org/W2916371586","https://openalex.org/W2920808503","https://openalex.org/W2937395761","https://openalex.org/W2943867078","https://openalex.org/W2944046905","https://openalex.org/W2951181218","https://openalex.org/W2968047181","https://openalex.org/W3080682237","https://openalex.org/W3090229172","https://openalex.org/W3121746194","https://openalex.org/W3151065533","https://openalex.org/W3161316917","https://openalex.org/W3217596308","https://openalex.org/W6658448023","https://openalex.org/W6673794245","https://openalex.org/W6681350118","https://openalex.org/W6686269225","https://openalex.org/W6762432331","https://openalex.org/W6762497819","https://openalex.org/W6766951835"],"related_works":["https://openalex.org/W2089504086","https://openalex.org/W4251733689","https://openalex.org/W4214952120","https://openalex.org/W1499147711","https://openalex.org/W2172134156","https://openalex.org/W2003455785","https://openalex.org/W613938734","https://openalex.org/W1582158723","https://openalex.org/W4385671403","https://openalex.org/W2952446579"],"abstract_inverted_index":{"In":[0],"this":[1,96],"paper,":[2],"a":[3,111,118],"type":[4],"of":[5,55,144],"high-order":[6],"compact":[7,69],"(HOC)":[8],"finite":[9],"difference":[10,31,70],"method":[11],"is":[12,33,46,64,74,87,98],"developed":[13],"for":[14,114,121],"solving":[15],"two-":[16],"and":[17,53,79,117],"three-dimensional":[18,103],"unsteady":[19,40,105],"convection":[20],"diffusion":[21],"reaction":[22],"(CDR)":[23],"equations":[24],"with":[25],"variable":[26],"coefficients.":[27],"Firstly,":[28],"an":[29],"HOC":[30],"scheme":[32,73,97],"derived":[34],"to":[35,100,139],"solve":[36,101,129],"the":[37,56,67,90,102,125,130,141,145],"two-dimensional":[38],"(2D)":[39],"CDR":[41,106],"equation.":[42,107,133],"Discretization":[43],"in":[44,62,77,82],"time":[45,78],"carried":[47],"out":[48],"by":[49,89],"Taylor":[50],"series":[51],"expansion":[52],"correction":[54],"truncation":[57],"error":[58],"remainder,":[59],"while":[60],"discretization":[61],"space":[63],"based":[65],"on":[66],"fourth-order":[68,80],"formulas.":[71],"The":[72,84],"second-order":[75],"accuracy":[76,81],"space.":[83],"unconditional":[85],"stability":[86],"obtained":[88],"von":[91],"Neumann":[92],"analysis":[93],"method.":[94],"Then,":[95],"extended":[99],"(3D)":[104],"It":[108],"needs":[109],"only":[110],"five-point":[112],"stencil":[113,120],"2D":[115],"problems":[116],"seven-point":[119],"3D":[122],"problems.":[123],"Moreover,":[124],"present":[126],"schemes":[127],"can":[128],"nonlinear":[131],"Burgers":[132],"Finally,":[134],"numerical":[135],"experiments":[136],"are":[137],"conducted":[138],"show":[140],"good":[142],"performances":[143],"new":[146],"schemes.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}