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Application of SDEs to estimating solutions to heat conduction equations with discontinuous coefficients

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Abstract

In this paper, numerical solutions to stochastic differential equations (SDEs) are proposed to be used for finding estimates of solutions to boundary value problems for linear parabolic equations with discontinuous coefficients. A generalized solution to a boundary value problem is approximated by the solution of the problem with smoothed coefficients. The results of calculations for a heat-protecting coating of a composite cellular material are presented.

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  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    S. A. Gusev

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  1. S. A. Gusev
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Correspondence to S. A. Gusev.

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Original Russian Text © S.A. Gusev, 2015, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2015, Vol. 18, No. 2, pp. 147–161.

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Gusev, S.A. Application of SDEs to estimating solutions to heat conduction equations with discontinuous coefficients. Numer. Analys. Appl. 8, 122–134 (2015). https://doi.org/10.1134/S1995423915020044

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