Application of SDE's to estimating the solution of heat equations with discontinuous coefficients
Sergey Anatol’evich Gusev
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentieva, 6, Novosibirsk, Russia, 630090
Keywords: heat equation, discontinuous coefficients, integral averaging, diffusion process, stochastic differential equations, Euler method
Abstract
This paper proposes the use of the numerical solution to stochastic differential equations (SDE's) to find estimates of the solutions to boundary value problems for linear parabolic equations with discontinuous coefficients. The solution of the problem with smoothed coefficients is taken as an approximation of the generalized solution to the considered boundary value problem. The results of calculations for a thermal barrier coating comprising a composite cellular material are presented.
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