Natural Volterra Runge-Kutta methods

Dajana Conte; Raffaele D'Ambrosio; Giuseppe Izzo; Zdzislaw Jackiewicz

doi:10.1007/s11075-013-9790-z

Natural Volterra Runge-Kutta methods

Dajana Conte, Raffaele D'Ambrosio, Giuseppe Izzo, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

20 Scopus citations

Abstract

A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for A- and V ₀-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.

Original language	English (US)
Pages (from-to)	421-445
Number of pages	25
Journal	Numerical Algorithms
Volume	65
Issue number	3
DOIs	https://doi.org/10.1007/s11075-013-9790-z
State	Published - Mar 2014

Keywords

A-stability
Order and stage order conditions
Stability analysis
V-stability
Volterra Runge-Kutta methods
Volterra integral equation

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-013-9790-z

Cite this

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title = "Natural Volterra Runge-Kutta methods",

abstract = "A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for A- and V 0-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.",

keywords = "A-stability, Order and stage order conditions, Stability analysis, V-stability, Volterra Runge-Kutta methods, Volterra integral equation",

author = "Dajana Conte and Raffaele D'Ambrosio and Giuseppe Izzo and Zdzislaw Jackiewicz",

note = "Funding Information: Partially supported by the School of Sciences and Technology - University of Naples “Federico II” under the project “F.A.R.O.” Control and stability of diffusive processes in the environment. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",

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doi = "10.1007/s11075-013-9790-z",

language = "English (US)",

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AU - Conte, Dajana

AU - D'Ambrosio, Raffaele

AU - Izzo, Giuseppe

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: Partially supported by the School of Sciences and Technology - University of Naples “Federico II” under the project “F.A.R.O.” Control and stability of diffusive processes in the environment. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

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N2 - A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for A- and V 0-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.

AB - A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for A- and V 0-stable methods is described and examples of highly stable methods are presented up to the order p = 4 and stage order q = 4.

KW - A-stability

KW - Order and stage order conditions

KW - Stability analysis

KW - V-stability

KW - Volterra Runge-Kutta methods

KW - Volterra integral equation

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JO - Numerical Algorithms

JF - Numerical Algorithms

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Natural Volterra Runge-Kutta methods

Abstract

Keywords

ASJC Scopus subject areas

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