Exponential splitting for unbounded operators
(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:
https://lup.lub.lu.se/record/1224128
- author
- Hansen, Eskil LU and Ostermann, Alexander
- publishing date
- 2009
- 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?
- no
- id
- d0369124-a8d4-46dd-8f7e-ef30f9bf1826 (old id 1224128)
- date added to LUP
- 2016-04-01 12:17:51
- date last changed
- 2024-08-14 21:30:46
@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}}, keywords = {{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}}, doi = {{10.1090/S0025-5718-09-02213-3}}, volume = {{78}}, year = {{2009}}, }