A Posteriori Analysis of a Multirate Numerical Method for Ordinary Differential Equations

Abstract. In this paper, we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model. We interpret the multirate method as a multiscale operator decomposition method and use this formulation to conduct both an a priori error analysis and a hybrid a priori-a posteriori error analysis. The hybrid analysis has the form of a computable a posteriori leading order expression and a provably-higher order a priori expression. Both analyses distinguish the effects of the discretization of each component from the effects of multirate solution. The effects on stability arising from the multirate solution are reflected in perturbations to certain associated adjoint operators.

Keywords. adjoint operator, a posteriori estimates, discontinuous Galerkin method, iterative method, multirate method, multiscale integration, operator decomposition