Stability of reducible quadrature methods for Volterra integral equations of the second kind

V. L. Bakke; Z. Jackiewicz

doi:10.1007/BF01389707

Stability of reducible quadrature methods for Volterra integral equations of the second kind

V. L. Bakke, Z. Jackiewicz

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

6 Scopus citations

Abstract

Stability analysis of reducible quadrature methods for Volterra integral equations based on the test equation {Mathematical expression} is presented. The concept of absolute stability is defined and necessary and sufficient conditions for the method to be absolutely stable for given λ, μ, and v are derived. These conditions are illustrated for the class of θ-methods for integral equations. The main tool in our stability analysis is the theory of difference equations of Poincaré type.

Original language	English (US)
Pages (from-to)	159-173
Number of pages	15
Journal	Numerische Mathematik
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/BF01389707
State	Published - Jun 1 1985
Externally published	Yes

Keywords

Subject Classifications: AMS (MOS): 65R20, CR: G1.9

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/BF01389707

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abstract = "Stability analysis of reducible quadrature methods for Volterra integral equations based on the test equation {Mathematical expression} is presented. The concept of absolute stability is defined and necessary and sufficient conditions for the method to be absolutely stable for given λ, μ, and v are derived. These conditions are illustrated for the class of θ-methods for integral equations. The main tool in our stability analysis is the theory of difference equations of Poincar{\'e} type.",

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N2 - Stability analysis of reducible quadrature methods for Volterra integral equations based on the test equation {Mathematical expression} is presented. The concept of absolute stability is defined and necessary and sufficient conditions for the method to be absolutely stable for given λ, μ, and v are derived. These conditions are illustrated for the class of θ-methods for integral equations. The main tool in our stability analysis is the theory of difference equations of Poincaré type.

AB - Stability analysis of reducible quadrature methods for Volterra integral equations based on the test equation {Mathematical expression} is presented. The concept of absolute stability is defined and necessary and sufficient conditions for the method to be absolutely stable for given λ, μ, and v are derived. These conditions are illustrated for the class of θ-methods for integral equations. The main tool in our stability analysis is the theory of difference equations of Poincaré type.

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Stability of reducible quadrature methods for Volterra integral equations of the second kind

Abstract

Keywords

ASJC Scopus subject areas

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