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High order splitting methods for analytic semigroups exist

Hansen, Eskil LU and Ostermann, Alexander (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)
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author
organization
publishing date
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
id
0828080c-91cf-4181-8f8e-0cab7b882cbd (old id 1485691)
date added to LUP
2009-11-12 10:19:12
date last changed
2017-12-10 04:23:24
@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},
  keyword      = {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},
  volume       = {49},
  year         = {2009},
}