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A method for efficient computation of optimal estimates in the extrapolation of solutions of nonlinear evolutionary differential equations in a Hilbert space. II

  • Systems Analysis
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Cybernetics and Systems Analysis Aims and scope

Abstract

The investigation pursued in the previous article is continued. Using a general algorithm of calculating the optimum prediction for a random process, an optimum extrapolation estimate is found in explicit form for the decision of a nonlinear evolutionary differential equation in a Hilbert space with unbounded linear operators. If a differential equation contains a small nonlinearity, then such an estimate is developed as a series in powers of a small parameter.

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References

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Authors and Affiliations

  1. Donetsk Economic-Humanitarian Institute, Donetsk, Ukraine

    A. A. Fomin-Shatashvili

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine

    A. D. Shatashvili

Authors
  1. A. A. Fomin-Shatashvili
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  2. A. D. Shatashvili
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Correspondence to A. A. Fomin-Shatashvili.

Additional information

Part I of this article is published in No. 3 (2008).

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 110–119, July–August 2008.

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Fomin-Shatashvili, A.A., Shatashvili, A.D. A method for efficient computation of optimal estimates in the extrapolation of solutions of nonlinear evolutionary differential equations in a Hilbert space. II. Cybern Syst Anal 44, 555–563 (2008). https://doi.org/10.1007/s10559-008-9026-8

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  • DOI: https://doi.org/10.1007/s10559-008-9026-8

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