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A second-order positivity preserving scheme for semilinear parabolic problems

Hansen, Eskil LU ; Kramer, Felix and Ostermann, Alexander (2012) In Applied Numerical Mathematics 62(10). p.1428-1435
Abstract
In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is shown that exponential operator splitting methods and in particular the method of Strang will preserve positivity in certain situations. A numerical illustration of the convergence behaviour is included.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
positivity, convergence, stability, semilinear parabolic problems, Strang splitting, invariant sets.
in
Applied Numerical Mathematics
volume
62
issue
10
pages
1428 - 1435
publisher
Elsevier
external identifiers
  • wos:000308685700014
  • scopus:84864612906
ISSN
0168-9274
DOI
10.1016/j.apnum.2012.06.003
language
English
LU publication?
yes
id
370ca544-bde6-490f-92c5-6d17f90f59b5 (old id 2971087)
date added to LUP
2012-09-21 18:31:09
date last changed
2017-10-20 19:49:58
@article{370ca544-bde6-490f-92c5-6d17f90f59b5,
  abstract     = {In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is shown that exponential operator splitting methods and in particular the method of Strang will preserve positivity in certain situations. A numerical illustration of the convergence behaviour is included.},
  author       = {Hansen, Eskil and Kramer, Felix and Ostermann, Alexander},
  issn         = {0168-9274},
  keyword      = {positivity,convergence,stability,semilinear parabolic problems,Strang splitting,invariant sets.},
  language     = {eng},
  number       = {10},
  pages        = {1428--1435},
  publisher    = {Elsevier},
  series       = {Applied Numerical Mathematics},
  title        = {A second-order positivity preserving scheme for semilinear parabolic problems},
  url          = {http://dx.doi.org/10.1016/j.apnum.2012.06.003},
  volume       = {62},
  year         = {2012},
}