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

Carmen Arévalo; Claus Führer; M Selva

doi:10.1016/S0168-9274(01)00138-6

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

Carmen Arévalo, Claus Führer, M Selva

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

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.

Originalspråk	engelska
Sidor (från-till)	5-16
Tidskrift	Applied Numerical Mathematics
Volym	42
Nummer	1-3
DOI	https://doi.org/10.1016/S0168-9274(01)00138-6
Status	Published - 2002

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

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Matematik

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title = "A collocation formulation of multistep methods for variable step-size extensions",

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.",

keywords = "step-size formulas, variable, ordinary differential equations (ODEs), multistep methods, collocation",

author = "Carmen Ar{\'e}valo and Claus F{\"u}hrer and M Selva",

note = "The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)",

year = "2002",

doi = "10.1016/S0168-9274(01)00138-6",

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AU - Arévalo, Carmen

AU - Führer, Claus

AU - Selva, M

N1 - The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - step-size formulas

KW - variable

KW - ordinary differential equations (ODEs)

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DO - 10.1016/S0168-9274(01)00138-6

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EP - 16

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 1-3

ER -

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

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