Geodesic
On a system of Volterra integral equations with a weakly singular kernel
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 33-44

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In this paper, we examine the existence and uniqueness of solutions for a system of Volterra integral equations with a weakly singular kernel. We approximate the solution of this system using the product integration method. The accuracy and efficiency of this method are illustrated in some numerical examples.
Keywords: nonlinear Volterra integral equation, integro-differential equation, fixed point, product integration method. 
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     title = {On a system of {Volterra} integral equations with a weakly singular kernel},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     year = {2021},
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M. Ghiat; S. Kamouche; A. Khellaf; W. Merchela. On a system of Volterra integral equations with a weakly singular kernel. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 33-44. http://geodesic.mathdoc.fr/item/INTO_2021_193_a5/