Iterative Operator Splitting Methods: Relation to Waveform Relaxation and Exponential Splitting Methods.

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 12 p.

MSC 2000

65M15 Error bounds

65L05 Initial value problems

Abstract
In this paper we describe a technique for closed formulation of an iterative operator-splitting method and embed the method in the classical exponential splitting methods. Since iterative operator splitting have been developed, an abstract framework to relate the method to other classical splitting methods is needed. Here an abstract framework considering the iterative splitting method as waveform-relaxation or exponential splitting method is devised. This is achieved by basing the analysis on semi-groups and fixed-point schemes. Abstract results illustrate differential equations with constant and time-dependent coefficients.