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Approximating the solution stochastic process of the random Cauchy one-dimensional heat model. (English) Zbl 1470.65153

Summary: This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
60H25 Random operators and equations (aspects of stochastic analysis)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
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