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04-03-2020 | Original Paper | Issue 1/2021

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

Journal:: Numerical Algorithms > Issue 1/2021

Authors:: Sayed Arsalan Sajjadi, Saeed Pishbin

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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.

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Title: Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels
Authors:: Sayed Arsalan Sajjadi
Saeed Pishbin
Publication date: 04-03-2020
DOI: https://doi.org/10.1007/s11075-020-00877-x
Publisher: Springer US
Journal: Numerical Algorithms
Issue 1/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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