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Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2021

04.03.2020 | Original Paper

Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels

verfasst von: Sayed Arsalan Sajjadi, Saeed Pishbin

Erschienen in: Numerical Algorithms | Ausgabe 1/2021

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Abstract

In this paper, we consider product integration method based on orthogonal polynomials to solve mixed system of Volterra integral equations of the first and second kind with weakly singular kernels. For investigation of the theoretical and numerical analysis of the mixed systems, the notions of the tractability index and ν-smoothing property are extended for a weakly singular Volterra integral operator. Convergence analysis of the product integration method is derived. Finally, the proposed method is illustrated by two examples, which confirm the theoretical prediction of the error estimation.
Vorheriger Artikel Adaptive total variation and second-order total variation-based model for low-rank tensor completion
Nächster Artikel Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces

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Metadaten
Titel
Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels
verfasst von
Sayed Arsalan Sajjadi
Saeed Pishbin
Publikationsdatum
04.03.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2021
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00877-x

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