A real distinct poles Exponential Time Differencing scheme for reaction-diffusion systems

A second order Exponential Time Differencing (ETD) method for reaction-diffusion systems which uses a real distinct poles discretization method for the underlying matrix exponentials is developed. The method is established to be stable and second order convergent. It is demonstrated to be robust for problems involving non-smooth initial and boundary conditions and steep solution gradients. We discuss several advantages over competing second order ETD schemes.