Structure-preserving numerical methods for highly nonlinear stochastic differential equations

题目:Structure-preserving numerical methods for highly nonlinear stochastic differential equations 

报告人:张中强教授,美国伍斯特理工学院,应用数学系 

时间:2018 年 7 月 31 日,星期二,下午 3 点 

地点:知新楼 B 座 924 

邀请人:王宏教授 

Abstract:Numerical methods are discussed for stochastic differential equations (SDEs) with local Lipschitz coefficients growing at most polynomially at infinity. We first review numerical methods for such nonlinear SDEs and then present our recent work on stability-preserving implicit schemes and explicit numerical schemes including modified forward Euler schemes and modified Milstein schemes. We also discuss some positivity-preserving schemes for SDEs with both local Lipschitz coefficients and Holder coefficients. Numerical comparison among various schemes for nonlinear SDEs is presented.