RUNGE-KUTTA TIME DISCRETIZATION OF REACTION-DIFFUSION AND NAVIER-STOKES EQUATIONS - NONSMOOTH-DATA ERROR-ESTIMATES AND APPLICATIONS TO LONG-TIME BEHAVIOR

We derive error bounds for Runge-Kutta time discretizations of. semili near parabolic equations with nonsmooth initial data. The framework in cludes reaction-diffusion equations and the incompressible Navier-Stok es equations. Nonsmooth-data error bounds of the type given here are n eeded in the study of the long-time behaviour of numerical discretizat ions. As an illustration, we use these low-order error bounds in provi ng high-order convergence of invariant closed curves of a Runge-Kutta method to periodic orbits of the parabolic problem.