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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 1, Pages 62–72 (Mi ivm8768)  

This article is cited in 15 scientific papers (total in 15 papers)

Solvability of systems of integral Volterra equations of the first kind with piecewise continuous kernels

D. N. Sidorovab

a Energy Systems Institute SB RAS, Irkutsk, Russia
b Chair of Mathematical Analysis and Differential Equations, Irkutsk State University, Irkutsk, Russia

Abstract: We construct an asymptotic approximation for solutions of systems of integral Volterra equations of the first kind with piecewise continuous kernel. We employ the asymptotics as an initial approximation in the proposed method of successive approximations to the desired solutions. We prove the existence of a continuous solution depending on free parameters and establish sufficient conditions for the existence of a unique continuous solution. We illustrate the proved existence theorems with examples.

Keywords: systems of integral Volterra equations of the first kind, asymptotics, continuous kernel, successive approximations.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:1, 54–63

UDC: 517.9
Received: 14.12.2011

Citation: D. N. Sidorov, “Solvability of systems of integral Volterra equations of the first kind with piecewise continuous kernels”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 1, 62–72; Russian Math. (Iz. VUZ), 57:1 (2013), 54–63

Citation in format AMSBIB
\Bibitem{Sid13}
\by D.~N.~Sidorov
\paper Solvability of systems of integral Volterra equations of the first kind with piecewise continuous kernels
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 1
\pages 62--72
\mathnet{http://mi.mathnet.ru/ivm8768}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 1
\pages 54--63
\crossref{https://doi.org/10.3103/S1066369X13010064}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872398312}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Markova, D. N. Sidorov, “On one integral Volterra model of developing dynamical systems”, Autom. Remote Control, 75:3 (2014), 413–421  mathnet  crossref  isi
    2. D. N. Sidorov, A. N. Tynda, I. R. Muftakhov, “Chislennoe reshenie integralnykh uravnenii Volterra I roda s kusochno-nepreryvnymi yadrami”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:3 (2014), 107–115  mathnet  crossref
    3. N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Math. Notes, 96:5 (2014), 811–826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. I. R. Muftakhov, D. N. Sidorov, N. A. Sidorov, “O regulyarizatsii po Lavrentevu integralnykh uravnenii pervogo roda v prostranstve nepreryvnykh funktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 15 (2016), 62–77  mathnet
    5. I. R. Muftahov, D. N. Sidorov, “Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels”, Bull. South Ural State U. Ser.-Math Model Program Comput., 9:1 (2016), 130–136  mathnet  zmath  isi
    6. T. A. Syed, V. P. Krishnan, J. Sivaswamy, “Numerical inversion of circular arc Radon transform”, IEEE Trans. Comput. Imaging, 2:4 (2016), 540–549  crossref  isi
    7. I. Muftahov, A. Tynda, D. Sidorov, “Numeric solution of Volterra integral equations of the first kind with discontinuous kernels”, J. Comput. Appl. Math., 313 (2017), 119–128  crossref  isi
    8. Assari P., Dehghan M., “a Meshless Local Discrete Galerkin (Mldg) Scheme For Numerically Solving Two-Dimensional Nonlinear Volterra Integral Equations”, Appl. Math. Comput., 350 (2019), 249–265  crossref  mathscinet  zmath  isi  scopus
    9. A. Tynda, D. Sidorov, I. Muftahov, “Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:4 (2020), 58–65  mathnet  crossref
    10. Noeiaghdam S., Dreglea A., He J., Avazzadeh Z., Suleman M., Fariborzi Araghi M.A., Sidorov D.N., Sidorov N., “Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations With Piecewise Smooth Kernels: Application of the Cadna Library”, Symmetry-Basel, 12:10 (2020), 1730  crossref  mathscinet  isi  scopus
    11. Sidorov D., Tynda A., Muftahov I., Dreglea A., Liu F., “Nonlinear Systems of Volterra Equations With Piecewise Smooth Kernels: Numerical Solution and Application For Power Systems Operation”, Mathematics, 8:8 (2020), 1257  crossref  isi  scopus
    12. Sidorov N., Sidorov D., Dreglea A., “Solvability and Bifurcation of Solutions of Nonlinear Equations With Fredholm Operator”, Symmetry-Basel, 12:6 (2020), 912  crossref  isi  scopus
    13. Kim G.H., Rassias T.M., “on the Stability of the Generalized Psi Functional Equation”, Axioms, 9:2 (2020), 58  crossref  isi  scopus
    14. Sidorov D., Muftahov I., Tomin N., Karamov D., Panasetsky D., Dreglea A., Liu F., Foley A., “a Dynamic Analysis of Energy Storage With Renewable and Diesel Generation Using Volterra Equations”, IEEE Trans. Ind. Inform., 16:5 (2020), 3451–3459  crossref  isi  scopus
    15. Noeiaghdam S., Sidorov D., Sizikov V., Sidorov N., “Control of Accuracy of Taylor-Collocation Method to Solve the Weakly Regular Volterra Integral Equations of the First Kind By Using the Cestac Method”, Appl. Comput. Math., 19:1 (2020), 87–105  mathscinet  zmath  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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