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Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels

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Abstract

For the Volterra equations with analytic kernels, we establish the exact power order of complexity of their approximate solutions and show that the optimal power order is realized by the method of simple iterations based on the use of information in the form of the values of kernels and free terms at certain points. In addition, for the Volterra equations with infinitely differentiable kernels, we determine the minimal order of the error of direct methods and construct a method which realizes this order.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    S. G. Solodkii

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  1. S. G. Solodkii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1534–1545, November, 1994.

The work was supported by the Foundation for Fundamental Researches of the Ukrainian State Committee on Science and Technology.

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Solodkii, S.G. Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels. Ukr Math J 46, 1695–1708 (1994). https://doi.org/10.1007/BF01058887

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  • DOI: https://doi.org/10.1007/BF01058887

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