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Error of the a-method for solving Volterra integral equations with polynomial nonlinearities

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Literature cited

  1. V. K. Dzyadyk, “An approximate method for the approximation of the solutions of linear differential equations by algebraic polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 4, 937–967 (1974).

    Google Scholar 

  2. V. K. Dzyadyk and L. I. Filozof, “The approximation by rational polynomials of the solutions of linear differential equations with polynomial coefficients,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 391–395 (1977).

    Google Scholar 

  3. V. K. Dzyadyk, “On the theory of special functions and their applications,” Mat. Sb.,131, No. 4, 438–464 (1986).

    Google Scholar 

  4. V. K. Dzyadyk and L. A. Ostrovetskii, “An approximation method for solving boundary value problems,” Ukr. Mat. Zh.,39, No. 3, 378–379 (1987).

    Google Scholar 

  5. A. P. Golub, Generalized Moment Representations and Rational Approximations [in Russian], Akad. Nauk Ukr. SSR, Inst. Mat., Kiev, Preprint No. 25 (1987).

  6. V. K. Dzyadyk, Approximation Methods for Solving Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  7. V. I. Bilenko, “An approximation method for solving integral equations with polynomial nonlinearities,” in: Integral Equations in Applied Modeling. Abstracts of Reports of the Second Republican Conference (Kiev, 1986) [in Russian], Inst. Electrodynamics, Academy of Sciences of the Ukrainian SSR, Kiev (1986), pp. 35–36.

    Google Scholar 

  8. V. I. Bilenko, “The a-method for solving Riccati differential equations,” in: Studies in the Theory of Approximation of Functions [in Russian], Inst. of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev (1987), pp. 5–13.

    Google Scholar 

  9. A. M. Basov, V. I. Bilenko, and A. I. Kashpirovskii, “The numerical implementation of the a-method for solving Riccati differential equations,” in: New Approaches for Solving Differential Equations. Abstracts of Reports. All-Union Conf. (Drogobych, 1987) [in Russian], Vychisl. Tsentr, Akad. Nauk SSSR, Moscow (1987), p. 7.

    Google Scholar 

  10. A. M. Basov, V. I. Bilenko, and A. I. Kashpirovskii, “The numerical implementation of the a-method for solving a certain class of Riccati differential equations,” in: Some Questions of the Theory of Approximation of Functions and Its Applications [in Russian], Inst. of Mathematics, Academy of Sciences of the Ukrainian SSSR, Kiev (1988), pp. 12–33.

    Google Scholar 

  11. K. I. Babenko, Foundations of Numerical Analysis [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  12. E. L. Ortiz and A. Pham Ngoc Dinh, “On the convergence of the Tau method for nonlinear differential equations of Riccati's type,” Nonlinear Anal. Theor. Methods Appl.,9, No. 1, 53–60 (1985).

    Google Scholar 

  13. G. E. Pukhov, “Prospective methods for the mathematical modeling of energy objects,” Vest. Akad. Nauk Ukranin SSR, No. 1, 10–20 (1988).

    Google Scholar 

  14. N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  15. S. N. Bernshtein, Extremal Properties of Polynomials and the Best Approximation of Continuous Functions of One Real Variable [in Russian], ONTI NKTP SSSR, Moscow (1937).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Problems of Modeling in Energetics, Academy of Sciences of the Ukrainian SSR, Kiev

    V. I. Bilenko

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  1. V. I. Bilenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 4, pp. 537–543, April, 1989.

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Bilenko, V.I. Error of the a-method for solving Volterra integral equations with polynomial nonlinearities. Ukr Math J 41, 467–472 (1989). https://doi.org/10.1007/BF01060627

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  • DOI: https://doi.org/10.1007/BF01060627

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