{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:28:11Z","timestamp":1759940891182},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We are interested in the numerical solution of\nstochastic differential equations with non-negative solutions. Our\ngoal is to construct explicit numerical schemes that preserve\npositivity, even for super-linear stochastic differential equations.\nIt is well known that the usual Euler scheme diverges on super-linear problems and\nthe tamed Euler method does not preserve positivity. In that\ndirection, we use the semi-discrete method that the first author has proposed in\ntwo previous papers. We propose a new numerical scheme for a class of stochastic differential equations\nwhich are super-linear with non-negative solution. The Heston 3\/2-model appearing in financial mathematics belongs to this class of stochastic differential equations. For this model we prove, through numerical experiments, the \u201coptimal\u201d order of strong convergence at least 1\/2 of the semi-discrete method.<\/jats:p>","DOI":"10.1515\/cmam-2015-0028","type":"journal-article","created":{"date-parts":[[2015,9,28]],"date-time":"2015-09-28T09:36:41Z","timestamp":1443433001000},"page":"105-132","source":"Crossref","is-referenced-by-count":16,"title":["On the Numerical Solution of Some Non-Linear Stochastic Differential Equations Using the Semi-Discrete Method"],"prefix":"10.1515","volume":"16","author":[{"given":"Nikolaos","family":"Halidias","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece"}]},{"given":"Ioannis S.","family":"Stamatiou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece"}]}],"member":"374","published-online":{"date-parts":[[2015,9,26]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/1\/article-p105.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0028\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0028\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:33:47Z","timestamp":1680298427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0028\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,1]]},"published-print":{"date-parts":[[2016,1,1]]}},"alternative-id":["10.1515\/cmam-2015-0028"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0028","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2015,9,26]]}}}