Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay
Hansen, Eskil LU
and Stillfjord, Tony
LU
(2014)
In BIT Numerical Mathematics
54(3).
p.673-689
- Abstract
- A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector field which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays fit into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) q = 1/2, without any artificial regularity assumptions. We discuss implementation details for the methods, and the convergence results are verified by numerical experiments demonstrating both the correct order, as well as the efficiency gain of Lie splitting as... (More)
- A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector field which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays fit into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) q = 1/2, without any artificial regularity assumptions. We discuss implementation details for the methods, and the convergence results are verified by numerical experiments demonstrating both the correct order, as well as the efficiency gain of Lie splitting as compared to the implicit Euler scheme. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4689579
- author
- Hansen, Eskil
LU
and Stillfjord, Tony
LU
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Nonlinear parabolic equations, delay differential equations, Convergence orders, Implicit Euler, Lie splitting
- in
- BIT Numerical Mathematics
- volume
- 54
- issue
- 3
- pages
- 673 - 689
- publisher
- Springer
- external identifiers
-
- wos:000342210300006
- scopus:84908097952
- ISSN
- 0006-3835
- DOI
- 10.1007/s10543-014-0480-6
- 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
- a27ffb5b-626b-40a8-b736-4e2ce555b82d (old id 4689579)
- alternative location
- http://link.springer.com/article/10.1007/s10543-014-0480-6
- date added to LUP
- 2016-04-01 10:31:25
- date last changed
- 2024-10-07 07:12:37
@article{a27ffb5b-626b-40a8-b736-4e2ce555b82d,
abstract = {{A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector field which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays fit into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) q = 1/2, without any artificial regularity assumptions. We discuss implementation details for the methods, and the convergence results are verified by numerical experiments demonstrating both the correct order, as well as the efficiency gain of Lie splitting as compared to the implicit Euler scheme.}},
author = {{Hansen, Eskil and Stillfjord, Tony}},
issn = {{0006-3835}},
keywords = {{Nonlinear parabolic equations; delay differential equations; Convergence orders; Implicit Euler; Lie splitting}},
language = {{eng}},
number = {{3}},
pages = {{673--689}},
publisher = {{Springer}},
series = {{BIT Numerical Mathematics}},
title = {{Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay}},
url = {{https://lup.lub.lu.se/search/files/1914070/4689584.pdf}},
doi = {{10.1007/s10543-014-0480-6}},
volume = {{54}},
year = {{2014}},
}