Solution of the Cauchy problem for anisotropic diffusion using stochastic and adaptive methods
This paper considers the Cauchy problem for an anisotropic diffusion equation. A stochastic representation of the solution based on Wiener processes is employed. Within a unified framework, the classical Monte Carlo method and an adaptive stochastic algorithm are analyzed. It is shown that the use of adaptive procedures significantly reduces the variance of estimators and improves computational efficiency. The results of numerical experiments confirm the theoretical findings and demonstrate the advantages of the proposed method. Keywords: anisotropic diffusion, Cauchy problem, stochastic methods, Monte Carlo method, adaptive algorithms.
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