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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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1569-3945
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Volume 11, Issue 5 (Dec 2003)

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On the solution of a class of Volterra integral equations of the first kind

F. Fagnani
  • Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: ,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ L. Pandolfi
  • Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: ,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

In this paper we propose an iterative algorithm for the solution of Volterra equations of the first kind whose kernel is a square matrix. The algorithm, essentially the Lavrientev method coupled with discretization, is "direct" in the sense that preliminary numerical computation of the derivative of the observed variable is not required. We assume boundedness of the input u and mild regularity conditions of the kernel. We prove convergence of the algorithm in L p(0, T), 1 ≤ p < +∞ and uniform convergence on the intervals where the input is continuous.

Under additional information on u we give both integral and pointwise convergence estimates.

The observed variable is read with errors, at discrete time instants.

About the article

Published Online:

Published in Print: 2003-12-01


Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939403770888237.

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A. Favini and L. Pandolfi
Journal of Inverse and Ill-posed Problems, 2008, Volume 16, Number 3

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