Asymptotic stability of solutions to Volterra-renewal integral equations with space maps

In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-11, Vol.395 (2), p.766-775
Main Authors: Annunziato, M., Brunner, H., Messina, E.
Format: Article
Language:English
Subjects:
Asymptotic behavior
Numerical methods
Renewal equation
Space map
Volterra integral equation
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Summary:In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. We show its properties through test examples.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.05.080