The well-known stochastic Lotka-Volterra model for interacting multi-species in ecology has some typical features: highly nonlinear, positive solution and multi-dimensional. The known numerical methods including the tamed/truncated Euler-Maruyama (EM) applied to it do not preserve its positivity. 
The aim of this talk is to modify the truncated EM to establish a new positive preserving truncated EM (PPTEM). To simplify the proof as well as to make our theory more understandable, we will first develop a nonnegative preserving truncated EM (NPTEM) and then establish the PPTEM. Of course, we should point out that the NPTEM has its own right as many SDE models in applications have their nonnegative solutions. 
This is a joint work with Xuerong Mao and Teerapot Wiriyakraikul.

魏凤英，福州大学数学与计算机科学学院教授，2006年7月博士毕业于东北师范大学应用数学专业。2007年获福州大学学术新人奖，2008年参加副校长范更华教授主持的离散数学及其应用“211工程”重点学科团队。曾主持国家自然科学基金两项、福建省自然科学基金三项；曾参与国家自然科学基金三项、教育部基金一项、福建省自然科学基金一项。目前累计发表及录用学术论文100余篇，其中SCI收录30余篇，国内一类及核心期刊收录60余篇。参加国内外学术会议及学术交流访问共计20余次，指导研究生共计26名，其中已毕业22名，4名在读。2014年破格评为教授，2015-2016年任芬兰赫尔辛基大学访问教授。现任福州大学数学系副主任，福建省生物数学学会第二届理事，主要研究随机微分方程及其在生物数学中的应用，包括流行病模型及阶段结构生态模型等。