|Zhongqiang Zhang, Mathematical Sciences, WPI|
|Title:Structure-preserving numerical methods fo highly nonlinear stochastic differential equations (SDEs)|
|Abstract:Numerical methods are discussed for 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.