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Exponential splitting for unbounded operators

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Author

Summary, in English

We present a convergence analysis for exponential splitting methods applied to linear evolution equations. Our main result states that the classical order of the splitting method is retained in a setting of unbounded operators, without requiring any additional order condition. This is achieved by basing the analysis on the

abstract framework of (semi)groups. The convergence analysis also includes generalizations to splittings consisting of more then two operators, and to variable time steps. We conclude by illustrating that the abstract results are applicable in the context of the Schrödinger equation with an external magnetic field or with an

unbounded potential.

Publishing year

2009

Language

English

Pages

1485-1496

Publication/Series

Mathematics of Computation

Volume

78

Issue

267

Document type

Journal article

Publisher

American Mathematical Society (AMS)

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • splitting schemes
  • convergence
  • nonstiff order
  • Schrödinger equation
  • unbounded operators
  • Exponential splitting

Status

Published

ISBN/ISSN/Other

  • ISSN: 1088-6842