Date of Award

August 2016

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Bruce Wade

Committee Members

Dexuan Xie, Tzu-chu Lin, Lei Wang, Peter Hinow


Advection Diffusion Reaction Equations, Dimensional Splitting, Exponential Time Differencing


A second order Exponential Time Differencing (ETD) scheme for advection-diffusion reaction systems is developed by using a real distinct poles rational function for approximating the underlying matrix exponential. The scheme is proved to be second order convergent. It is demonstrated to be robust for reaction-diffusion systems with non-smooth initial and boundary conditions, sharp solution gradients, and stiff reaction terms. In order to apply the scheme efficiently to higher dimensional problems, a dimensional splitting technique is also developed. This technique can be applied to all ETD schemes and has been found, in the test problems considered, to reduce computational time by up to 80%.