{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T09:22:25Z","timestamp":1789723345562,"version":"4.0.1"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100007780","name":"Kyushu Institute of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["23540143"],"award-info":[{"award-number":["23540143"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We propose new explicit exponential Runge--Kutta methods for the weak approximation of solutions of stiff It\u00f4 stochastic differential equations (SDEs). We also consider the use of exponential Runge--Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2.<\/jats:p>","DOI":"10.1137\/15m1041341","type":"journal-article","created":{"date-parts":[[2017,12,12]],"date-time":"2017-12-12T13:35:15Z","timestamp":1513085715000},"page":"A2857-A2878","source":"Crossref","is-referenced-by-count":20,"title":["Weak Second Order Explicit Exponential Runge--Kutta Methods for Stochastic Differential Equations"],"prefix":"10.1137","volume":"39","author":[{"given":"Yoshio","family":"Komori","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Cohen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Burrage","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,12,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/070679375"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2008.v6.n4.a3"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100292"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-013-0430-8"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/12088954X"},{"key":"atypb6","unstructured":"I. 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Adamu,\n                      Numerical Approximation of SDEs and Stochastic Swift-Hohenberg Equation\n                      , Ph.D. thesis, Heriot-Watt University, Edinburgh, UK, 2011."},{"key":"atypb7","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold L.","year":"1974"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2012.03.002"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0426-8"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/17442509508833962"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2008.03.012"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/16.1.11"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/140994204"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-011-9273-z"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/070700607"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022355410570"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595295337"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/040611434"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000048"},{"key":"atypb20","unstructured":"P. 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