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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: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 446-470, 2024/08/29
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