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A collocation formulation of multistep methods for variable step-size extensions

Arévalo, Carmen LU ; Führer, Claus LU and Selva, M (2002) In Applied Numerical Mathematics 42(1-3). p.5-16
Abstract
Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid. To make them practically useful, they have to be implemented by varying the step-size according to some error-control algorithm. It is well known how to extend Adams and BDF formulas to a variable step-size formulation. In this paper we present a collocation approach to construct variable step-size formulas. We make use of piecewise polynomials to show that every k-step method of order k + I has a variable step-size polynomial collocation formulation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
step-size formulas, variable, ordinary differential equations (ODEs), multistep methods, collocation
in
Applied Numerical Mathematics
volume
42
issue
1-3
pages
5 - 16
publisher
Elsevier
external identifiers
  • wos:000177312100002
  • scopus:0036680041
ISSN
0168-9274
DOI
10.1016/S0168-9274(01)00138-6
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
b1bc8f31-334a-4f21-9ec7-318b7332d3c5 (old id 331818)
date added to LUP
2016-04-01 15:41:00
date last changed
2022-02-27 08:13:53
@article{b1bc8f31-334a-4f21-9ec7-318b7332d3c5,
  abstract     = {{Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid. To make them practically useful, they have to be implemented by varying the step-size according to some error-control algorithm. It is well known how to extend Adams and BDF formulas to a variable step-size formulation. In this paper we present a collocation approach to construct variable step-size formulas. We make use of piecewise polynomials to show that every k-step method of order k + I has a variable step-size polynomial collocation formulation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.}},
  author       = {{Arévalo, Carmen and Führer, Claus and Selva, M}},
  issn         = {{0168-9274}},
  keywords     = {{step-size formulas; variable; ordinary differential equations (ODEs); multistep methods; collocation}},
  language     = {{eng}},
  number       = {{1-3}},
  pages        = {{5--16}},
  publisher    = {{Elsevier}},
  series       = {{Applied Numerical Mathematics}},
  title        = {{A collocation formulation of multistep methods for variable step-size extensions}},
  url          = {{http://dx.doi.org/10.1016/S0168-9274(01)00138-6}},
  doi          = {{10.1016/S0168-9274(01)00138-6}},
  volume       = {{42}},
  year         = {{2002}},
}