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Characterization of the rate of convergence of one approximate method for the solution of an abstract Cauchy problem

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Ukrainian Mathematical Journal Aims and scope

Abstract

We consider an approximate method for the solution of the Cauchy problem for an operator differential equation. This method is based on the expansion of an exponential in orthogonal Laguerre polynomials. We prove that the fact that an initial value belongs to a certain space of smooth elements of the operator A is equivalent to the convergence of a certain weighted sum of integral residuals. As a corollary, we obtain direct and inverse theorems of the theory of approximation in the mean.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    S. M. Torba

  2. “Kyevo-Mohylyans’ka Akademiya” National University, Kyiv, Ukraine

    O. I. Kashpirovs’kyi

Authors
  1. S. M. Torba
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  2. O. I. Kashpirovs’kyi
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 557–563, April, 2008.

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Torba, S.M., Kashpirovs’kyi, O.I. Characterization of the rate of convergence of one approximate method for the solution of an abstract Cauchy problem. Ukr Math J 60, 639–647 (2008). https://doi.org/10.1007/s11253-008-0073-0

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  • DOI: https://doi.org/10.1007/s11253-008-0073-0

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