An ETD Crank‐Nicolson method for reaction‐diffusion systems

A novel Exponential Time Differencing Crank‐Nicolson method is developed which is stable, second‐order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity‐preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012