A collocation formulation of multistep methods for variable step-size extensions
(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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https://lup.lub.lu.se/record/331818
- author
- Arévalo, Carmen LU ; Führer, Claus LU and Selva, M
- organization
- publishing date
- 2002
- 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}}, }