{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T01:15:29Z","timestamp":1772759729087,"version":"3.50.1"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"China Natural National Science Foundation","award":["91630201"],"award-info":[{"award-number":["91630201"]}]},{"name":"China Natural National Science Foundation","award":["11971198"],"award-info":[{"award-number":["11971198"]}]},{"name":"China Natural National Science Foundation","award":["11871245"],"award-info":[{"award-number":["11871245"]}]},{"name":"China Natural National Science Foundation","award":["11771179"],"award-info":[{"award-number":["11771179"]}]},{"name":"China Natural National Science Foundation","award":["11826101"],"award-info":[{"award-number":["11826101"]}]},{"name":"Program for Cheung Kong Scholars","award":["Q2016067"],"award-info":[{"award-number":["Q2016067"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s40314-019-0990-6","type":"journal-article","created":{"date-parts":[[2019,11,18]],"date-time":"2019-11-18T11:02:01Z","timestamp":1574074921000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Analysis of continuous collocation solutions for nonlinear functional equations with vanishing delays"],"prefix":"10.1007","volume":"39","author":[{"given":"Jian","family":"Tian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hehu","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ran","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,13]]},"reference":[{"key":"990_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543234","volume-title":"Collocation methods for volterra integral and related functional differential equations","author":"H Brunner","year":"2004","unstructured":"Brunner H (2004) Collocation methods for volterra integral and related functional differential equations. Cambridge University Press, Cambridge"},{"key":"990_CR2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s11464-009-0001-0","volume":"4","author":"H Brunner","year":"2009","unstructured":"Brunner H (2009) Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Front. Math. China 4:3\u201322","journal-title":"Front. Math. China"},{"key":"990_CR3","doi-asserted-by":"crossref","unstructured":"Brunner H, Xie HH, Zhang R (2010) Analysis of collocation solutions for a class of functional equations with proportional delays. IMA J Numer Anal. (to appear)","DOI":"10.1093\/imanum\/drp051"},{"key":"990_CR4","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1093\/imamat\/8.3.271","volume":"8","author":"L Fox","year":"1971","unstructured":"Fox L, Mayers DF, Ockendon JR, Tayler AB (1971) On a functional differential equation. J. Inst. Math. Appl. 8:271\u2013307","journal-title":"J. Inst. Math. Appl."},{"key":"990_CR5","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/j.cam.2016.11.005","volume":"317","author":"L Hui","year":"2017","unstructured":"Hui L, Yang Z, Gao J (2017) Strong superconvergence of the Euler\u2013Maruyama method for linear stochastic Volterra integral equations. J Comput Appl Math 317:447\u2013457","journal-title":"J Comput Appl Math"},{"key":"990_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0956792500000966","volume":"4","author":"A Iserles","year":"1993","unstructured":"Iserles A (1993) On the generalized pantograph functional differential equation. European J Appl Math 4:1\u201338","journal-title":"European J Appl Math"},{"key":"990_CR7","first-page":"133","volume":"1","author":"A Iserles","year":"1994","unstructured":"Iserles A (1994) Numerical analysis of delay differential equations with variable delays. Ann Numer Math 1:133\u2013152","journal-title":"Ann Numer Math"},{"key":"990_CR8","volume-title":"Beyond the classical theory of computational ordinary differential equations","author":"A Iserles","year":"1997","unstructured":"Iserles A (1997) The state of the art in numerical analysis. In: Duff IS, Watson GA (eds) Beyond the classical theory of computational ordinary differential equations. Clarendon Press, Oxford"},{"key":"990_CR9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative methods for linear and nonlinear equations","author":"CT Kelley","year":"1995","unstructured":"Kelley CT (1995) Iterative methods for linear and nonlinear equations. SIAM, Philadelphia"},{"key":"990_CR10","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0893-9659(94)00103-J","volume":"8","author":"Y-K Liu","year":"1995","unstructured":"Liu Y-K (1995) The linear $$q$$ difference equation $$y(x)=ay(qx)+f(x)$$. Appl Math Lett 8:15\u201318","journal-title":"Appl Math Lett"},{"key":"990_CR11","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF02580504","volume":"25","author":"V Volterra","year":"1897","unstructured":"Volterra V (1897) Sopra alcune questioni di inversione di integrali definite. Ann Math Pura Appl 25:139\u20131178","journal-title":"Ann Math Pura Appl"},{"issue":"6","key":"990_CR12","doi-asserted-by":"publisher","first-page":"3303","DOI":"10.1137\/100818595","volume":"33","author":"HH Xie","year":"2011","unstructured":"Xie HH, Zhang R, Brunner H (2011) Collocation methods for general Volterra functional integral equations with vanishing delays. SIAM J Sci Comput 33(6):3303\u20133332","journal-title":"SIAM J Sci Comput"},{"key":"990_CR13","first-page":"507","volume":"21","author":"Z Yang","year":"2014","unstructured":"Yang Z, Brunner H (2014) Quenching analysis for nonlinear Volterra integral equations. Dyn Contin Discrete Impuls Syst Ser A Math Anal 21:507\u2013529","journal-title":"Dyn Contin Discrete Impuls Syst Ser A Math Anal"},{"key":"990_CR14","doi-asserted-by":"publisher","first-page":"977","DOI":"10.1016\/j.jmaa.2019.06.061","volume":"479","author":"H Yang","year":"2019","unstructured":"Yang H, Yang Z, Wang P, Han D (2019) Mean-square stability analysis for nonlinear stochastic pantograph equations by transformation approach. J Math Anal Appl 479:977\u2013986","journal-title":"J Math Anal Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0990-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-0990-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0990-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,12]],"date-time":"2020-11-12T00:51:59Z","timestamp":1605142319000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-0990-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,13]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["990"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-0990-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,13]]},"assertion":[{"value":"7 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"23"}}