{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T06:20:28Z","timestamp":1789712428298,"version":"4.0.1"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) $d[x(t)-u(x_t)]=f(x_t)dt+g(x_t)dw(t)$, $t\\geq 0$. The key contribution is to establish the strong mean square convergence theory of the Euler\u2013Maruyama approximate solution under the local Lipschitz condition, the linear growth condition, and contractive mapping. These conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here are obtained under quite general conditions. Although the way of analysis borrows from [X. Mao, LMS J. Comput. Math., 6 (2003), pp. 141\u2013161], to cope with $u(x_t)$, several new techniques have been developed.<\/jats:p>","DOI":"10.1137\/070697021","type":"journal-article","created":{"date-parts":[[2008,4,16]],"date-time":"2008-04-16T18:05:23Z","timestamp":1208369123000},"page":"1821-1841","source":"Crossref","is-referenced-by-count":71,"title":["Numerical Solutions of Neutral Stochastic Functional Differential Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Fuke","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuerong","family":"Mao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,16]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.07.010"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157000000322"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01395814"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00475-1"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(97)00035-4"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1078415836"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0721036"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"P. E. Kloeden and E. Platen,\n                      Numerical Solutions of Stochastic Differential Equations\n                      , Springer, Berlin, 1992.","DOI":"10.1007\/978-3-662-12616-5"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(00)00224-X"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(99)00021-3"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S003614299731867X"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1080\/01630569408816550"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(95)00018-5"},{"key":"R14","unstructured":"X. Mao,\n                      Stochastic Differential Equations and Applications\n                      , Horwood, Chichester, 1997."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141095290835"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157000000425"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(02)00750-1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.02.030"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070697021","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:04Z","timestamp":1787325244000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070697021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070697021"],"URL":"https:\/\/doi.org\/10.1137\/070697021","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}