Operator splitting methods for stiff convection-reaction-diffusion equations

Abstract: 

For reaction-diffusion systems with both stiff reaction and diffusion terms, the implicit integration factor (IIF) method and its high dimensional analog compact form (cIIF) serve as an efficient class of time-stepping methods. For nonlinear hyperbolic equations, front tracking method is one of the most powerful tools to dynamically track the sharp interfaces. Meanwhile, weighted essentially non-oscillatory (WENO) methods are a class of start-of-the-art schemes with uniform high order of accuracy in smooth regions of the solution. In this talk, IIF/cIIF is coupled with front tracking or WENO by the second-order symmetric operator splitting approach to solve advection-reaction-dffusion equations. In the methods, IIF/cIIF methods treat the stiff reaction-diffusion equations, and front tracking/WENO methods handlehyperbolic equations that arise from the advection part.

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