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A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

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Abstract

In this work, we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels. Particularly, we consider the case when the underlying solutions are sufficiently smooth. In this case, the proposed method leads to a fully discrete linear system. We show that the fully discrete integral operator is stable in both infinite and weighted square norms. Furthermore, we establish that the approximate solution arrives at an optimal convergence order under the two norms. Finally, we give some numerical examples, which confirm the theoretical prediction of the exponential rate of convergence.

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  1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 2500014, China

    HaoTao Cai

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  1. HaoTao Cai
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Cai, H. A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels. Sci. China Math. 57, 2163–2178 (2014). https://doi.org/10.1007/s11425-014-4806-2

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