{"id":"https://openalex.org/W2164733373","doi":"https://doi.org/10.1137/040607058","title":"General Linear Methods for Volterra Integro-differential Equations with Memory","display_name":"General Linear Methods for Volterra Integro-differential Equations with Memory","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2164733373","doi":"https://doi.org/10.1137/040607058","mag":"2164733373"},"language":"en","primary_location":{"id":"doi:10.1137/040607058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607058","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/133235","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101737392","display_name":"Chengjian Zhang","orcid":"https://orcid.org/0000-0001-9016-5631"},"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":true,"raw_author_name":"Chengjian Zhang","raw_affiliation_strings":["Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, 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":["Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101737392"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":4.9777,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.95362752,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"27","issue":"6","first_page":"2010","last_page":"2031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9988999962806702,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8152997493743896},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.6586996912956238},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6304094195365906},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.5979092121124268},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5557825565338135},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5287339687347412},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5190140008926392},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5074657797813416},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4722694158554077},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.46086108684539795},{"id":"https://openalex.org/keywords/integro-differential-equation","display_name":"Integro-differential equation","score":0.45856061577796936},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.43100035190582275},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.42550963163375854},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41014406085014343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34396445751190186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3209187984466553},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2801501452922821},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.19449850916862488},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.12224581837654114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11615726351737976},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.07509219646453857}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152997493743896},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6586996912956238},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6304094195365906},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.5979092121124268},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5557825565338135},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5287339687347412},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5190140008926392},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5074657797813416},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4722694158554077},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.46086108684539795},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.45856061577796936},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.43100035190582275},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.42550963163375854},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41014406085014343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34396445751190186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3209187984466553},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2801501452922821},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.19449850916862488},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.12224581837654114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11615726351737976},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.07509219646453857},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040607058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607058","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.500.2905","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.500.2905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://lirias.kuleuven.be/bitstream/123456789/133235/1/SISC27(6)Zhangdw.pdf","raw_type":"text"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/133235","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/133235","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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 Scientific Computing, vol. 27 (6), Art.No. 6, (2010-2031)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/133235","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/133235","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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 Scientific Computing, vol. 27 (6), Art.No. 6, (2010-2031)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W138803476","https://openalex.org/W166472065","https://openalex.org/W170982414","https://openalex.org/W273294507","https://openalex.org/W596378822","https://openalex.org/W1550341792","https://openalex.org/W1970448574","https://openalex.org/W1970476229","https://openalex.org/W1978082100","https://openalex.org/W1978848077","https://openalex.org/W1982536042","https://openalex.org/W2003281488","https://openalex.org/W2008007187","https://openalex.org/W2009724929","https://openalex.org/W2009865300","https://openalex.org/W2017639176","https://openalex.org/W2020478360","https://openalex.org/W2036393825","https://openalex.org/W2037658016","https://openalex.org/W2043734742","https://openalex.org/W2046314344","https://openalex.org/W2047038715","https://openalex.org/W2053972515","https://openalex.org/W2054748390","https://openalex.org/W2063738015","https://openalex.org/W2064369834","https://openalex.org/W2066855895","https://openalex.org/W2069595440","https://openalex.org/W2070571304","https://openalex.org/W2093478476","https://openalex.org/W2524994179","https://openalex.org/W2737633787","https://openalex.org/W2981569720","https://openalex.org/W3021895250"],"related_works":["https://openalex.org/W2086430948","https://openalex.org/W2517153600","https://openalex.org/W4318069473","https://openalex.org/W1979313496","https://openalex.org/W2047521779","https://openalex.org/W2800810559","https://openalex.org/W2921812035","https://openalex.org/W2050964714","https://openalex.org/W2164733373","https://openalex.org/W3129744708"],"abstract_inverted_index":{"A":[0],"new":[1],"class":[2],"of":[3,21,37,40,57],"numerical":[4,46,59],"methods":[5,15,24],"for":[6],"Volterra":[7],"integro-differential":[8],"equations":[9],"with":[10,25],"memory":[11],"is":[12],"developed.":[13],"The":[14],"are":[16,48],"based":[17],"on":[18],"the":[19,38,41,53,58],"combination":[20],"general":[22],"linear":[23],"compound":[26],"quadrature":[27],"rules.":[28],"Sufficient":[29],"conditions":[30],"that":[31],"guarantee":[32],"global":[33],"and":[34,44,55],"asymptotic":[35],"stability":[36],"solution":[39],"differential":[42],"equation":[43],"its":[45],"approximation":[47],"established.":[49],"Numerical":[50],"examples":[51],"illustrate":[52],"convergence":[54],"effectiveness":[56],"methods.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}