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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
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
id
b1bc8f31-334a-4f21-9ec7-318b7332d3c5 (old id 331818)
date added to LUP
2007-08-02 11:45:52
date last changed
2017-02-13 13:07:13
@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},
  keyword      = {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},
  volume       = {42},
  year         = {2002},
}