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Exponential splitting for unbounded operators

Hansen, Eskil LU and Ostermann, Alexander (2009) In Mathematics of Computation 78(267). p.1485-1496
Abstract
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
splitting schemes, convergence, nonstiff order, Schrödinger equation, unbounded operators, Exponential splitting
in
Mathematics of Computation
volume
78
issue
267
pages
1485 - 1496
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:67749119705
ISSN
1088-6842
DOI
10.1090/S0025-5718-09-02213-3
language
English
LU publication?
yes
id
d0369124-a8d4-46dd-8f7e-ef30f9bf1826 (old id 1224128)
date added to LUP
2008-09-02 10:52:46
date last changed
2017-10-01 03:51:55
@article{d0369124-a8d4-46dd-8f7e-ef30f9bf1826,
  abstract     = {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<br/><br>
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<br/><br>
unbounded potential.},
  author       = {Hansen, Eskil and Ostermann, Alexander},
  issn         = {1088-6842},
  keyword      = {splitting schemes,convergence,nonstiff order,Schrödinger equation,unbounded operators,Exponential splitting},
  language     = {eng},
  number       = {267},
  pages        = {1485--1496},
  publisher    = {American Mathematical Society (AMS)},
  series       = {Mathematics of Computation},
  title        = {Exponential splitting for unbounded operators},
  url          = {http://dx.doi.org/10.1090/S0025-5718-09-02213-3},
  volume       = {78},
  year         = {2009},
}