Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions

Author(s): Wang, Dongyong | Advisor(s): Nie, Qing | Abstract: Reaction diffusion equations are widely used to model biological phenomena and in some situation, the spatial dimension can be much larger. Numerical efficiently solving high-dimensional reaction-diffusion equations is a huge challenge. To solve the high-dimensional equation, the ``curse of dimensions" has to be dealt with. Also, an efficiently time integration method is needed to solve the afterwords time dependent problem. The sparse grid technique can deal with the problem, and the semi-implicit integration factor method can handles the second one. The combination of two methods will be an efficient method to solve high-dimensional reaction-diffusion equations.