{"id":"https://openalex.org/W2169378796","doi":"https://doi.org/10.1137/s0036142902419296","title":"Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation","display_name":"Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2169378796","doi":"https://doi.org/10.1137/s0036142902419296","mag":"2169378796"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902419296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902419296","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://lirias.kuleuven.be/handle/123456789/133395","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100651262","display_name":"Chengming Huang","orcid":"https://orcid.org/0000-0001-8556-1111"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengming Huang","raw_affiliation_strings":["Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Stefan Vandewalle","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Computerscience, Celestijnenlaan 200A, B3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computerscience, Celestijnenlaan 200A, B3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8323,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94406172,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"5","first_page":"2020","last_page":"2042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9983000159263611,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8814586400985718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6173155307769775},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5860997438430786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5583102703094482},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5463353991508484},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5405738353729248},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5341581106185913},{"id":"https://openalex.org/keywords/pantograph","display_name":"Pantograph","score":0.514435350894928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34841716289520264},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06185072660446167}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8814586400985718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6173155307769775},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5860997438430786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5583102703094482},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5463353991508484},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5405738353729248},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5341581106185913},{"id":"https://openalex.org/C20756127","wikidata":"https://www.wikidata.org/wiki/Q722757","display_name":"Pantograph","level":2,"score":0.514435350894928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34841716289520264},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06185072660446167},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142902419296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902419296","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:lirias2repo.kuleuven.be:123456789/133395","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/133395","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","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":"SIAM Journal on Numerical Analysis, vol. 42 (5), Art.No. 5, (2020-2042)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/133395","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/133395","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","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":"SIAM Journal on Numerical Analysis, vol. 42 (5), Art.No. 5, (2020-2042)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W29277913","https://openalex.org/W170982414","https://openalex.org/W1509923322","https://openalex.org/W1550341792","https://openalex.org/W1969409177","https://openalex.org/W1979146918","https://openalex.org/W1982536042","https://openalex.org/W1991877218","https://openalex.org/W1992147499","https://openalex.org/W2007716695","https://openalex.org/W2009309548","https://openalex.org/W2017595816","https://openalex.org/W2019317114","https://openalex.org/W2021997456","https://openalex.org/W2035460619","https://openalex.org/W2050171503","https://openalex.org/W2063738015","https://openalex.org/W2076024467","https://openalex.org/W2081442517","https://openalex.org/W2110829009","https://openalex.org/W2111471396","https://openalex.org/W2128358316","https://openalex.org/W2142472783","https://openalex.org/W2169303215","https://openalex.org/W2409760985","https://openalex.org/W2410615660","https://openalex.org/W2481497112","https://openalex.org/W4293515545"],"related_works":["https://openalex.org/W2408472582","https://openalex.org/W2378529747","https://openalex.org/W4387011711","https://openalex.org/W2372731345","https://openalex.org/W2057677727","https://openalex.org/W2787802451","https://openalex.org/W2360526382","https://openalex.org/W2379657325","https://openalex.org/W4252833549","https://openalex.org/W2732220824"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,25,62],"concerned":[3],"with":[4,19],"the":[5,12,41,45,59,79],"stability":[6,43,74],"properties":[7],"of":[8,44,48,81,86],"Runge--Kutta":[9],"methods":[10,67],"for":[11,40,58,64],"pantograph":[13,51],"equation,":[14],"a":[15,20,82],"functional":[16],"differential":[17],"equation":[18],"proportional":[21],"delay.":[22],"The":[23],"focus":[24],"on":[26],"nonautonomous":[27],"equations.":[28,71,87],"Both":[29],"linear":[30],"and":[31,37],"nonlinear":[32],"cases":[33],"are":[34,53,76],"considered.":[35],"Sufficient":[36],"necessary":[38],"conditions":[39],"asymptotic":[42],"numerical":[46],"solution":[47],"general":[49,84],"neutral":[50],"equations":[52],"given.":[54],"An":[55],"upper":[56],"bound":[57],"error":[60],"growth":[61],"investigated":[63],"algebraically":[65],"stable":[66],"applied":[68],"to":[69,78],"nonneutral":[70],"Finally,":[72],"some":[73],"results":[75],"extended":[77],"case":[80],"more":[83],"class":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}