Operator splitting method Overlapping operator splitting methods Schwarz alternating methods Consistency and stability analysis Parabolic equations Overlapping operator splitting methods and applications in stiff differential equations. Juergen Geiser Geiser Juergen Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 12 p.

Overlapping operator splitting methods and applications in stiff differential equations.

Juergen Geiser

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

MSC 2000

35K45 Initial value problems for parabolic systems
35K90 Abstract parabolic evolution equations

Abstract
In this article we study the stability of an overlapping operator-splitting methods based on iterative methods. We discuss the overlapping iterative Operator Splitting method in the context of decoupling the stiff and non-stiff operators. In the context of stabilisation the stiff operators, we present the overlapping ideas as extension to the standard iterative operator splitting method. The efficiency of considering the overlapping method instead of the standard method whole domain in the is discussed. We apply our theoretical results on model problems in stiff parabolic partial differential equations.

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