Iterative operator-splitting method: Error analysis and examples

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 24 pp.

MSC 2000

65M15 Error bounds

65L05 Initial value problems

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