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The error structure of the Douglas-Rachford splitting method for stiff linear problems

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Author

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.

Department/s

Publishing year

2016-03-02

Language

English

Publication/Series

Journal of Computational and Applied Mathematics

Document type

Journal article

Publisher

Elsevier

Topic

  • Other Mathematics

Keywords

  • Douglas–Rachford splitting
  • error analysis
  • order reduction
  • stiff linear problems
  • inhomogeneous evolution equations
  • dissipative operators.

Status

Published

Research group

  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0377-0427