Iterative Operator Splitting Methods For Differential Equations: Prooftechniques And Applications

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 34 pp.

MSC 2000

65M15 Error bounds

65L05 Initial value problems

Abstract
In this paper we describe an iterative operator-splitting method for bounded operators. Our contribution is a novel iterative method that can be applied as a splitting method to ordinary and partial differential equations. A simple relation between the number of iterative steps and order of the splitting scheme makes this an alternative method to a time decomposition method. The iterative splitting scheme can be applied to a physical problem, but the original problem is not divided as in standard splitting schemes. We present error bounds for iterative splitting methods in the presence of bounded operators. We discuss efficient algorithms for computing the integral formulation of the splitting scheme. In experiments, we consider the benefits of the novel splitting method in terms of the number of iterations and time steps. Ordinary differential equations and convection-diffusion-reaction equations are presented in the numerical results.