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Numerical Solution of A Class of Systems of Volterra Polynomial Equations of the First Kind

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Abstract

In this paper, a class of second-order systems of Volterra nonlinear integral equations is considered. This class is related to a problem of automatic control of a dynamic object with vector inputs and outputs. A numerical solution technique based on the Newton–Kantorovich method is considered. To verify the efficiency of the algorithms developed, a series of test calculations are carried out.

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References

  1. Giannakins, G.B. and Serpedin, E., A Bibliography on Nonlinear System Identification, Sign. Process., 2001, vol. 81, pp. 533–580.

    Article  MATH  Google Scholar 

  2. Tsibizova, T.Yu., Identification Methods for Nonlinear Control Systems, Modern Probl. Sci. Educ., 2015, no. 1 (part 1), pp. 109–116; https: //www.science-education.ru/ru/article/view?id=17910.

    Google Scholar 

  3. Volkov, N.V., Funktsional’nye ryady v zadachakh dinamiki avtomatizirovannykh sistem (Functional Series in Problems of Dynamics of Automated Systems), Moscow: Yanus-K, 2001.

    Google Scholar 

  4. Volterra, V., A Theory of Functionals, Integral and Integro-Differential Equations, New York: Dover Publ., 1959.

    MATH  Google Scholar 

  5. Brunner, H., Volterra Integral Equations: An Introduction to Theory and Applications, Cambridge: Cambridge University Press, 2017.

    Book  MATH  Google Scholar 

  6. Apartsin, A.S., Studying the Polynomial Volterra Equation of the First Kind for Solution Stability, Autom. Remote Contr., 2011, vol. 72, no. 6, pp. 1229–1236.

    Article  MathSciNet  MATH  Google Scholar 

  7. Apartsin, A.S., Multilinear Integral Volterra Equations of the First Kind: Elements of Theory and Numeric Methods, Izv. Irkutsk. Gos. Univ. Mat., 2007, no. 1, pp. 13–41.

    Google Scholar 

  8. Apartsin, A.S., On the Convergence of Numerical Methods for Solving a Volterra Bilinear Equation of the First Kind, Comput. Math.Math. Phys., 2007, vol. 47, no. 8, pp. 1323–1331.

    Article  MathSciNet  Google Scholar 

  9. Apartsin, A.S., Multilinear Volterra Equations of the First Kind, Autom. Remote Contr., 2004, vol. 65, no. 2, pp. 263–269.

    Article  MathSciNet  Google Scholar 

  10. Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz v normirovannykh prostranstvakh (Functional Analysis in Normed Spaces), Moscow: Fizmatlit, 1959.

    MATH  Google Scholar 

  11. Solodusha, S.V., A Class of Systems of Bilinear Integral Volterra Equations of the First Kind of the Second Order, Autom. Remote Contr., 2009, vol. 70, no. 4, pp. 663–671.

    Article  MathSciNet  MATH  Google Scholar 

  12. Bel’tyukov, B.A., Solving Nonlinear Integral Equations by Newton’s Method, Diff. Ur., 1966, vol. 2, no. 8, pp. 1072–1083.

    MathSciNet  Google Scholar 

  13. Boikov, I.V. and Tynda, A.N., Approximate Solution of Nonlinear Integral Equations of the Theory of Developing Systems, Diff. Eq., 2003, vol. 39, no. 9, pp. 1277–1288.

    Article  MathSciNet  MATH  Google Scholar 

  14. Tairov, E.A., Nonlinear Simulation of Heat Exchange Dynamics in a Duct with a Single-Phase Heat Carrier, Izv. AN SSSR. Energ. Trans., 1989, no. 1, pp. 150–156.

    Google Scholar 

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Authors and Affiliations

  1. Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 130, Irkutsk, 664033, Russia

    S. V. Solodusha

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  1. S. V. Solodusha
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Correspondence to S. V. Solodusha.

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Original Russian Text © S.V. Solodusha, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 1, pp. 117–126.

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Solodusha, S.V. Numerical Solution of A Class of Systems of Volterra Polynomial Equations of the First Kind. Numer. Analys. Appl. 11, 89–97 (2018). https://doi.org/10.1134/S1995423918010093

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  • DOI: https://doi.org/10.1134/S1995423918010093

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