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Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies

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Abstract

We consider a boundary-value problem of mechanics of inhomogeneous hereditarily elastic bodies formulated as a linear equation with an operator of fractional integration, partial derivatives with respect to time and spatial variables, and polynomial-type coefficients of one of the variables. An approximate solution of this problem is constructed according to Dzyadyk's a-method combined with the use of the Laplace transformation. It is proved that the errors of the approximation of the required function and its derivatives decrease in geometric progression.

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Authors and Affiliations

  1. Dnepropetrovsk Mining Institute, Dnepropetrovsk

    E. S. Sinaiskii

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  1. E. S. Sinaiskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1234–1245, September, 1994.

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Sinaiskii, E.S. Approximation method for the problems of mechanics of inhomogeneous hereditarily elastic bodies. Ukr Math J 46, 1356–1368 (1994). https://doi.org/10.1007/BF01059426

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  • DOI: https://doi.org/10.1007/BF01059426

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