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On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions

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Abstract

The approximate solution of the Volterra integral equation of the second kind is represented as collocation rational spline functions on successive closed intervals exhausting the entire solution domain. Estimates for the rate of convergence of approximate solutions to the exact solution in the uniform metric are also obtained via the modulus of continuity of the solution and its derivatives of first and second order.

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Authors and Affiliations

  1. Daghestan State University, Makhachkala, 367025, Russia

    A.-R. K. Ramazanov & V. G. Magomedova

  2. Daghestan Federal Research Center of Russian Academy of Sciences, Makhachkala, 367000, Russia

    A.-R. K. Ramazanov

  3. Kaluga Branch of Bauman Moscow State Technical University, Kaluga, 248004, Russia

    A. K. Ramazanov

Authors
  1. A.-R. K. Ramazanov
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  2. A. K. Ramazanov
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  3. V. G. Magomedova
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Correspondence to A.-R. K. Ramazanov.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 581-591 https://doi.org/10.4213/mzm13303.

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Ramazanov, AR.K., Ramazanov, A.K. & Magomedova, V.G. On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions. Math Notes 111, 595–603 (2022). https://doi.org/10.1134/S0001434622030282

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  • DOI: https://doi.org/10.1134/S0001434622030282

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