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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5-16
Journal	Applied Numerical Mathematics
Volume	42
Issue number	1-3
DOIs	https://doi.org/10.1016/S0168-9274(01)00138-6
Publication status	Published - 2002

Bibliographical 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)

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

step-size formulas
variable
ordinary differential equations (ODEs)
multistep methods
collocation

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10.1016/S0168-9274(01)00138-6

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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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T1 - A collocation formulation of multistep methods for variable step-size extensions

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)

KW - multistep methods

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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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