Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
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On the solution of a class of Volterra integral equations of the first kind
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 11, Issue 5, Pages 485–503, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939403770888237,
- Published Online:
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.
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