演讲专家：Qing Nie，University of California Irvine，USA 

演讲主题：Numerical methods for stiff reaction-diffusion-advection equations. 

演讲时间：2015年10月20日，10:00-11:00 am  

演讲地点：环境学院316房间 

报告摘要： For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction–diffusion systems with both stiff reaction and diffusion terms, here we present a new class of implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF), in which their second order version is linearly unconditionally stable. For the equation with advection term, we use splitting methods to incorporate different numerical methods for different terms to improve stability property.  Applications of the methods to several biological systems demonstrate that the overall method is accurate and efficient.