A second-order positivity preserving scheme for semilinear parabolic problems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2971087
- author
- Hansen, Eskil LU ; Kramer, Felix and Ostermann, Alexander
- organization
- publishing date
- 2012
- 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
- 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
- 370ca544-bde6-490f-92c5-6d17f90f59b5 (old id 2971087)
- date added to LUP
- 2016-04-01 11:16:24
- date last changed
- 2024-08-13 17:29:13
@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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/2524144/2971108.pdf}}, doi = {{10.1016/j.apnum.2012.06.003}}, volume = {{62}}, year = {{2012}}, }