Overlapping Operator-Splitting Methods with Higher-Order Splitting Methods and Applications in Stiff Differential Equations

In this article, we combine operator-splitting methods of an iterative and non-iterative type to problems for stiff differential equations. The time-splitting is performed with operator-splitting methods and the spatial splitting is done with an overlapping Schwarz waveform relaxation, see [Daoud/Geiser 2006] and [Farago/Geiser 2005]. We discuss the iterative and non-iterative operator-splitting method in the context of achieving higher-order accuracy and with respect to stiff matrices. We discuss the stability of each decomposition method and influence of the higher-order approach via Richardson extrapolation. The stability analysis is presented and the benefit of the iterative method is discussed. At least we discuss the future work and the conclusions to our wor