operator splitting Schwarz waveform relaxation method higher order methods stability analysis iterative methods Overlapping Operator-Splitting Methods with Higher-Order Splitting Methods and Applications in Stiff Differential Equations. Juergen Geiser Geiser Juergen Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 11 pp.

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

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 11 pp.

MSC 2000

35J60 Nonlinear PDE of elliptic type
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE

Abstract
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 work.

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