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Runge-Kutta Restarters for Multistep Methods in Presence of Frequent Discontinuities

Mohammadi, Fatemeh LU ; Arévalo, Carmen LU and Führer, Claus LU (2017) In Journal of Computational and Applied Mathematics 316. p.287-297
Abstract
Differential equations with discontinuities or differential equations coupled to discrete systems require frequent re-initializations of the numerical solution process. The classical starting process of multistep methods, based on increasing the order in the initialization phase, is computationally expensive when frequent discontinuities occur. Instead we propose to use the stage values or weight vectors of these specially constructed explicit Runge–Kutta methods for starting processes. Two practical examples demonstrate these methods.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Multistep Methods, Error estimation, Runge–Kutta methods, Discontinuities
in
Journal of Computational and Applied Mathematics
volume
316
pages
287 - 297
publisher
Elsevier
external identifiers
  • scopus:85006093164
  • wos:000392784600023
ISSN
0377-0427
DOI
10.1016/j.cam.2016.09.042
language
English
LU publication?
yes
id
a8110737-d152-4ffc-a799-89385f4e0b61
date added to LUP
2017-01-25 10:59:20
date last changed
2018-01-07 11:46:46
@article{a8110737-d152-4ffc-a799-89385f4e0b61,
  abstract     = {Differential equations with discontinuities or differential equations coupled to discrete systems require frequent re-initializations of the numerical solution process. The classical starting process of multistep methods, based on increasing the order in the initialization phase, is computationally expensive when frequent discontinuities occur. Instead we propose to use the stage values or weight vectors of these specially constructed explicit Runge–Kutta methods for starting processes. Two practical examples demonstrate these methods.},
  author       = {Mohammadi, Fatemeh and Arévalo, Carmen and Führer, Claus},
  issn         = {0377-0427},
  keyword      = {Multistep Methods,Error estimation,Runge–Kutta methods,Discontinuities},
  language     = {eng},
  month        = {05},
  pages        = {287--297},
  publisher    = {Elsevier},
  series       = {Journal of Computational and Applied Mathematics},
  title        = {Runge-Kutta Restarters for Multistep Methods in Presence of Frequent Discontinuities},
  url          = {http://dx.doi.org/10.1016/j.cam.2016.09.042},
  volume       = {316},
  year         = {2017},
}