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

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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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  1. Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran

    Sayed Arsalan Sajjadi & Saeed Pishbin

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  1. Sayed Arsalan Sajjadi
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  2. Saeed Pishbin
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Correspondence to Saeed Pishbin.

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Sajjadi, S.A., Pishbin, S. Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels. Numer Algor 86, 25–54 (2021). https://doi.org/10.1007/s11075-020-00877-x

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  • DOI: https://doi.org/10.1007/s11075-020-00877-x

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