{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:51Z","timestamp":1787333271681,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We consider stochastic Runge\u2013Kutta methods for It\u00f4 stochastic ordinary differential equations, and study their mean-square convergence properties for problems with small multiplicative noise or additive noise. First we present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations, and a Maruyama term is used to discretize the diffusion. Further, we suggest improving the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals, and we present a suitable class of fully derivative-free methods. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth the effort. Simulation results illustrate the theoretical findings.<\/jats:p>","DOI":"10.1137\/090763275","type":"journal-article","created":{"date-parts":[[2010,6,20]],"date-time":"2010-06-20T21:18:25Z","timestamp":1277068705000},"page":"1789-1808","source":"Crossref","is-referenced-by-count":25,"title":["Stochastic Runge\u2013Kutta Methods for It\u00f4 SODEs with Small Noise"],"prefix":"10.1137","volume":"32","author":[{"given":"Evelyn","family":"Buckwar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"R\u00f6\u00dfler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renate","family":"Winkler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,6,18]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"S. Artemiev and T. Averina,\n                      Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations\n                      , VSP BV, Utrecht, The Netherlands, 1997.","DOI":"10.1515\/9783110944662"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157000000322"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.200410004"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/040602857"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.03.038"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(96)00027-X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(98)00042-7"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999363206"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1023\/B:BITN.0000025089.50729.0f"},{"key":"R10","unstructured":"P. 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