This article is cited in 10 papers

Application of SDE's to estimating the solution of heat equations with discontinuous coefficients

S. A. Gusev

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia

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.

Key words: heat equation, discontinuous coefficients, integral averaging, diffusion process, stochastic differential equations, Euler method.

UDC: 519.676

Received: 16.09.2014
Revised: 30.10.2014

DOI: 10.15372/SJNM20150204

 English version: Numerical Analysis and Applications, 2015, 8:2, 122–134

Bibliographic databases:

• 
•