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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)
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author
organization
publishing date
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
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
2014-10-23 19:31:33
date last changed
2017-11-12 03:08:48
@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},
  keyword      = {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          = {http://dx.doi.org/10.1007/s10543-014-0480-6},
  volume       = {54},
  year         = {2014},
}