Geodesic
Multi-step methods for the numerical solution of integro-algebraic equations with two singularities in the 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 – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 104-114

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We consider a class of Volterra integro-algebraic equations with two integrable power singularities in the kernel and indicate fundamental difficulties in studying such equations. In terms of matrix pencils, we formulate sufficient conditions for the existence of a unique continuous solution. Also, we propose multi-step methods for solving such equations based on the method of integrating products and Adams quadrature formulas and present the results of numerical experiments.
Keywords: Volterra integro-algebraic equation; multi-step method; boundary singularity; diagonal singularity; rank-degree criterion. 
@article{INTO_2022_204_a10,
     author = {S. S. Orlov and O. S. Budnikova and M. N. Botoroeva},
     title = {Multi-step methods for the numerical solution of integro-algebraic equations with two singularities in the kernel},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {104--114},
     publisher = {mathdoc},
     volume = {204},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_204_a10/}
}
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S. S. Orlov; O. S. Budnikova; M. N. Botoroeva. Multi-step methods for the numerical solution of integro-algebraic equations with two singularities in the 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 – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 104-114. http://geodesic.mathdoc.fr/item/INTO_2022_204_a10/