{"id":"https://openalex.org/W1976760067","doi":"https://doi.org/10.1137/s0036142999361505","title":"A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations","display_name":"A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1976760067","doi":"https://doi.org/10.1137/s0036142999361505","mag":"1976760067"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999361505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361505","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://scholars.cityu.edu.hk/ws/files/189065734/5011008.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087806562","display_name":"Heping Ma","orcid":"https://orcid.org/0000-0002-8891-7635"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Heping Ma","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014226512","display_name":"Weiwei Sun","orcid":"https://orcid.org/0000-0002-2079-4480"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weiwei Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087806562"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6928,"has_fulltext":true,"cited_by_count":94,"citation_normalized_percentile":{"value":0.93357016,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"38","issue":"5","first_page":"1425","last_page":"1438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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":0.9991999864578247,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8397011756896973},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.8209947347640991},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.7810890674591064},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5992398858070374},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5946645736694336},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5879821181297302},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5180854797363281},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5055241584777832},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.4914745092391968},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.48564162850379944},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.449584037065506},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4484458565711975},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.4405971169471741},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41045302152633667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4072212874889374},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3961877226829529},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.37871959805488586},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.23457834124565125},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.14619004726409912},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1428147554397583},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.08938196301460266},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05785861611366272}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8397011756896973},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.8209947347640991},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.7810890674591064},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5992398858070374},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5946645736694336},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5879821181297302},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5180854797363281},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5055241584777832},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.4914745092391968},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.48564162850379944},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.449584037065506},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4484458565711975},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.4405971169471741},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41045302152633667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4072212874889374},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3961877226829529},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.37871959805488586},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.23457834124565125},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.14619004726409912},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1428147554397583},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.08938196301460266},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05785861611366272},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142999361505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361505","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/0fad5707-8a35-4491-84f6-cf3932bcfd5d","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/0fad5707-8a35-4491-84f6-cf3932bcfd5d","pdf_url":"https://scholars.cityu.edu.hk/ws/files/189065734/5011008.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ma, H & Sun, W 2001, 'A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations', SIAM Journal on Numerical Analysis, vol. 38, no. 5, pp. 01425-1438.","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/0fad5707-8a35-4491-84f6-cf3932bcfd5d","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/0fad5707-8a35-4491-84f6-cf3932bcfd5d","pdf_url":"https://scholars.cityu.edu.hk/ws/files/189065734/5011008.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ma, H & Sun, W 2001, 'A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations', SIAM Journal on Numerical Analysis, vol. 38, no. 5, pp. 01425-1438.","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1976760067.pdf","grobid_xml":"https://content.openalex.org/works/W1976760067.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W638558759","https://openalex.org/W810778011","https://openalex.org/W1975478888","https://openalex.org/W1995277785","https://openalex.org/W2011355268","https://openalex.org/W2013059590","https://openalex.org/W2017403023","https://openalex.org/W2023105121","https://openalex.org/W2023988191","https://openalex.org/W2032988056","https://openalex.org/W2045475603","https://openalex.org/W2046683716","https://openalex.org/W2052169332","https://openalex.org/W2055623556","https://openalex.org/W2069381275","https://openalex.org/W2070066621","https://openalex.org/W2075931789","https://openalex.org/W2082849992","https://openalex.org/W2131778920","https://openalex.org/W2169437869","https://openalex.org/W2408478130","https://openalex.org/W2410898212","https://openalex.org/W2999792156","https://openalex.org/W3150423993","https://openalex.org/W4298060601","https://openalex.org/W4300846967"],"related_works":["https://openalex.org/W1482343169","https://openalex.org/W4206513033","https://openalex.org/W2296924041","https://openalex.org/W2179563627","https://openalex.org/W2890254931","https://openalex.org/W2135245226","https://openalex.org/W2136729106","https://openalex.org/W2172024322","https://openalex.org/W1848947320","https://openalex.org/W3048174355"],"abstract_inverted_index":{"A":[0],"Legendre--Petrov--Galerkin":[1,65],"(LPG)":[2],"method":[3,17,39],"for":[4,58],"the":[5,16,48,54,59,77],"third-order":[6],"differential":[7],"equation":[8,52],"is":[9,40,63],"developed.":[10],"By":[11],"choosing":[12],"appropriate":[13],"base":[14],"functions,":[15],"can":[18],"be":[19],"implemented":[20],"efficiently.":[21],"Also,":[22],"this":[23],"new":[24],"approach":[25],"enables":[26],"us":[27],"to":[28,42,75],"derive":[29],"an":[30],"optimal":[31],"rate":[32],"of":[33],"convergence":[34],"in":[35],"L2":[36],"-norm.":[37],"The":[38],"applied":[41],"some":[43],"nonlinear":[44,60],"problems":[45],"such":[46],"as":[47],"Korteweg--de":[49],"Vries":[50],"(KdV)":[51],"with":[53],"Chebyshev":[55,67],"collocation":[56,68],"treatment":[57],"term.":[61],"It":[62],"a":[64],"and":[66],"(LPG-CC)":[69],"method.":[70],"Numerical":[71],"experiments":[72],"are":[73],"given":[74],"confirm":[76],"theoretical":[78],"result.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
