High order splitting methods for analytic semigroups exist
(2009) In BIT Numerical Mathematics 49(3). p.527-542- Abstract
- In this paper, we are concerned with the construction and analysis of high order exponential splitting methods for the time integration of abstract evolution equations which are evolved by analytic semigroups. We derive a new class of splitting methods of orders three to fourteen based on complex coefficients. An optimal convergence analysis is presented for the methods when applied to equations on Banach spaces with unbounded vector fields. These results resolve the open question whether there exist splitting schemes with convergence rates greater then two in the context of semigroups. As a concrete application we consider parabolic equations and their dimension splittings. The sharpness of our theoretical error bounds is further... (More)
- In this paper, we are concerned with the construction and analysis of high order exponential splitting methods for the time integration of abstract evolution equations which are evolved by analytic semigroups. We derive a new class of splitting methods of orders three to fourteen based on complex coefficients. An optimal convergence analysis is presented for the methods when applied to equations on Banach spaces with unbounded vector fields. These results resolve the open question whether there exist splitting schemes with convergence rates greater then two in the context of semigroups. As a concrete application we consider parabolic equations and their dimension splittings. The sharpness of our theoretical error bounds is further illustrated by numerical experiments. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1485691
- author
- Hansen, Eskil LU and Ostermann, Alexander
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- High order convergence, Exponential splitting methods, Analytic semigroups, Parabolic equations
- in
- BIT Numerical Mathematics
- volume
- 49
- issue
- 3
- pages
- 527 - 542
- publisher
- Springer
- external identifiers
-
- wos:000270448500005
- scopus:70350425793
- ISSN
- 0006-3835
- DOI
- 10.1007/s10543-009-0236-x
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- 0828080c-91cf-4181-8f8e-0cab7b882cbd (old id 1485691)
- date added to LUP
- 2016-04-01 15:01:57
- date last changed
- 2022-01-28 03:43:10
@article{0828080c-91cf-4181-8f8e-0cab7b882cbd,
abstract = {{In this paper, we are concerned with the construction and analysis of high order exponential splitting methods for the time integration of abstract evolution equations which are evolved by analytic semigroups. We derive a new class of splitting methods of orders three to fourteen based on complex coefficients. An optimal convergence analysis is presented for the methods when applied to equations on Banach spaces with unbounded vector fields. These results resolve the open question whether there exist splitting schemes with convergence rates greater then two in the context of semigroups. As a concrete application we consider parabolic equations and their dimension splittings. The sharpness of our theoretical error bounds is further illustrated by numerical experiments.}},
author = {{Hansen, Eskil and Ostermann, Alexander}},
issn = {{0006-3835}},
keywords = {{High order convergence; Exponential splitting methods; Analytic semigroups; Parabolic equations}},
language = {{eng}},
number = {{3}},
pages = {{527--542}},
publisher = {{Springer}},
series = {{BIT Numerical Mathematics}},
title = {{High order splitting methods for analytic semigroups exist}},
url = {{http://dx.doi.org/10.1007/s10543-009-0236-x}},
doi = {{10.1007/s10543-009-0236-x}},
volume = {{49}},
year = {{2009}},
}