Abstract:
Some algorithm is presented for solving the convolution type Volterra integral equation of the first kind by the quadrature-sum method. We assume that the integral equation of the first kind cannot be reduced to an integral equation of the second kind
but we do not assume that either the kernel or some of its derivatives at zero are unequal to zero. For the relations we propose there is given an estimate of the error of the calculated solution. Some examples of numerical experiments are presented
to demonstrate the efficiency of the algorithm.
Keywords:
integral Volterra equation, convolution type equation, numerical solution.
Citation:
A. L. Karchevsky, “Solution of the convolution type Volterra integral equations
of the first kind by the quadrature-sum method”, Sib. Zh. Ind. Mat., 23:3 (2020), 40–52; J. Appl. Industr. Math., 14:3 (2020), 503–512
\Bibitem{Kar20}
\by A.~L.~Karchevsky
\paper Solution of the convolution type Volterra integral equations
of the first kind by the quadrature-sum method
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 3
\pages 40--52
\mathnet{http://mi.mathnet.ru/sjim1097}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.304}
\elib{https://elibrary.ru/item.asp?id=44282777}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 503--512
\crossref{https://doi.org/10.1134/S1990478920030096}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094681805}
Linking options:
https://www.mathnet.ru/eng/sjim1097
https://www.mathnet.ru/eng/sjim/v23/i3/p40
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