Numerical treatment of a Volterra integral equation with space maps

Authors:
Mario Annunziato;Eleonora Messina
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy;Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, I-80126 Napoli, Italy
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

In this paper we consider linear Volterra Integral Equations (VIEs) whose solution depends on a space variable, via a map transformation. We investigate on the basic qualitative properties of this kind of equation, and introduce a numerical method based on direct quadrature along time and interpolation for space. For this method we study the convergence and we show its performances on some test examples.