• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

Verlag der Österreichischen Akademie der Wissenschaften
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ETNA - Electronic Transactions on Numerical Analysis



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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Error analysis of a Jacobi modified projection-type method for weakly singular Volterra-Hammerstein integral equations

    Hamza Bouda, Chafik Allouch, Kapil Kant, Zakaria El Allali

ETNA - Electronic Transactions on Numerical Analysis, pp. 446-470, 2024/08/29

doi: 10.1553/etna_vol60s446

doi: 10.1553/etna_vol60s446


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doi:10.1553/etna_vol60s446



doi:10.1553/etna_vol60s446

Abstract

The paper proposes polynomial-based projection-type and modified projection-type methods to solve weakly singular Volterra–Hammerstein integral equations of the second kind. Jacobi polynomials are used as basis functions. This type of equations often exhibits singular behavior at the left endpoint of the integration interval, and the exact solutions are typically nonsmooth. In the method under consideration, the independent variable is first transformed to provide a new integral equation with a smoother solution, allowing the Jacobi spectral method to be easily applied to the transformed equation and a full convergence analysis of the method to be performed. In different numerical tests, the effectiveness of the proposed approach is demonstrated.

Keywords: Volterra–Hammerstein integral equations Jacobi polynomials weakly singular kernels orthogonal interpolatory projection superconvergence