On Volterra like integral equations coming from statistical process monitoring

Junghanns, Peter; Knoth, Sven

doi:10.3934/mcrf.2025017

On Volterra like integral equations coming from statistical process monitoring

Publication date

2025-03-08

Document type

Forschungsartikel

Author

Junghanns, Peter

Knoth, Sven

Organisational unit

Rechnergestützte Statistik

DOI

10.3934/mcrf.2025017

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/21935

Scopus ID

2-s2.0-105016107993

Publisher

American Institute of Mathematical Sciences (AIMS)

Series or journal

Mathematical Control and Related Fields

ISSN

2156-8499

Periodical volume

15

Periodical issue

4

First page

1444

Last page

1469

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Keyword

Collocation-quadrature method

Fredholm integral equation

Gaussian rule

Statistical process monitoring

Abstract

We consider a Fredholm integral equation of the second kind on the interval (0, 1) in which the integral operator (Formula presented) has a variable integral limit of the form αz with 0 < α < 1, and g<inf>β</inf>(x) has an algebraic singularity at x = 0. In the case of α = 1, the above integral operator would be a Volterra integral operator of convolution type. That is why we call K<inf>β</inf> a Volterra-like operator if 0 < α < 1. We propose a fully discrete collocation-quadrature method for its numerical solution using a Gaussian rule for the interval (0, 1) transformed onto the variable interval. Stability of the method and convergence rates for the approximating solutions are proved and compared with the respective pure collocation method (which, of course, is not a fully discrete method).

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Published version

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