The error structure of the Douglas-Rachford splitting method for stiff linear problems
Författare
Summary, in English
The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is con- sidered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure. This gives rise to order reductions if the evolution equation does not satisfy extra compatibility assumptions. To remedy the situation one can add correction-terms to the splitting scheme which, e.g., yields the first-order Douglas–Rachford (DR) scheme. In this paper we derive a rigorous error analysis in the setting of linear dissipative operators and inhomo- geneous evolution equations. We also illustrate the order reduction of the Lie splitting, as well as the far superior performance of the DR splitting.
Avdelning/ar
- Matematik LTH
- Numerical Analysis
Publiceringsår
2016-03-02
Språk
Engelska
Publikation/Tidskrift/Serie
Journal of Computational and Applied Mathematics
Fulltext
- Available as PDF - 233 kB
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Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Other Mathematics
Nyckelord
- Douglas–Rachford splitting
- error analysis
- order reduction
- stiff linear problems
- inhomogeneous evolution equations
- dissipative operators.
Status
Published
Forskningsgrupp
- Numerical Analysis
ISBN/ISSN/Övrigt
- ISSN: 0377-0427