{"id":"https://openalex.org/W1975666830","doi":"https://doi.org/10.1090/s0025-5718-99-01059-5","title":"Error estimation of Hermite spectral method for nonlinear partial differential equations","display_name":"Error estimation of Hermite spectral method for nonlinear partial differential equations","publication_year":1999,"publication_date":"1999-02-05","ids":{"openalex":"https://openalex.org/W1975666830","doi":"https://doi.org/10.1090/s0025-5718-99-01059-5","mag":"1975666830"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01059-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01059-5","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01059-5/S0025-5718-99-01059-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01059-5/S0025-5718-99-01059-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112630309","display_name":"Ben\u2010yu Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ben-yu Guo","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, China","Department of Mathematics, Shanghai University, Jiading Campus, Shanghai, 201800, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Jiading Campus, Shanghai, 201800, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112630309"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":4.6671,"has_fulltext":true,"cited_by_count":148,"citation_normalized_percentile":{"value":0.94879332,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"68","issue":"227","first_page":"1067","last_page":"1078"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.993399977684021,"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":0.9087165594100952},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.8846707940101624},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6151731610298157},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6030758619308472},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5576639175415039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5264393091201782},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5221710205078125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4538109302520752},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.45165950059890747},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4405113458633423},{"id":"https://openalex.org/keywords/hermite-spline","display_name":"Hermite spline","score":0.421691358089447},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.4194231629371643},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0609300434589386},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05960315465927124}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9087165594100952},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8846707940101624},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6151731610298157},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6030758619308472},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5576639175415039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5264393091201782},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5221710205078125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4538109302520752},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.45165950059890747},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4405113458633423},{"id":"https://openalex.org/C186763157","wikidata":"https://www.wikidata.org/wiki/Q5741918","display_name":"Hermite spline","level":5,"score":0.421691358089447},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.4194231629371643},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0609300434589386},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05960315465927124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.0},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-99-01059-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01059-5","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01059-5/S0025-5718-99-01059-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.102.3807","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.3807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1999-68-227/S0025-5718-99-01059-5/S0025-5718-99-01059-5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01059-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01059-5","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01059-5/S0025-5718-99-01059-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975666830.pdf","grobid_xml":"https://content.openalex.org/works/W1975666830.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1500096885","https://openalex.org/W1971743999","https://openalex.org/W1985849492","https://openalex.org/W2013282326","https://openalex.org/W2046899724","https://openalex.org/W2047035089","https://openalex.org/W2065378774","https://openalex.org/W2072653497","https://openalex.org/W2199665742","https://openalex.org/W2380304257","https://openalex.org/W4249558853","https://openalex.org/W4255465707","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1611524765","https://openalex.org/W2358067891","https://openalex.org/W1993375521","https://openalex.org/W1758105233","https://openalex.org/W2888610286","https://openalex.org/W2383451251","https://openalex.org/W60612525","https://openalex.org/W4287669264","https://openalex.org/W3083777569","https://openalex.org/W2562925856"],"abstract_inverted_index":{"Hermite":[0,15],"approximation":[1,10],"is":[2,18],"investigated.":[3],"Some":[4],"inverse":[5],"inequalities,":[6],"imbedding":[7],"inequalities":[8],"and":[9,25],"results":[11],"are":[12,31,40],"obtained.":[13],"A":[14],"spectral":[16],"scheme":[17,30],"constructed":[19],"for":[20],"Burgers":[21],"equation.":[22],"The":[23,34],"stability":[24],"convergence":[26],"of":[27],"the":[28],"proposed":[29],"proved":[32],"strictly.":[33],"techniques":[35],"used":[36],"in":[37,47],"this":[38],"paper":[39],"also":[41],"applicable":[42],"to":[43],"other":[44],"nonlinear":[45],"problems":[46],"unbounded":[48],"domains.":[49]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}