Geodesic
Information processing in a numerical study for some stochastic Wentzell systems of the hydrodynamic equations in a ball and on its boundary
Journal of computational and engineering mathematics, Tome 11 (2024) no. 3, pp. 3-15.

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In this paper we study stochastic Wentzell systems: filtration equations describing fluid filtration processes in a fractured porous medium in a three-dimensional ball and on its boundary; free filtration equations describing the evolution of the free surface of the filtered fluid in a three-dimensional ball and on its boundary. In particular, numerical solutions of the Cauchy problem are constructed for the above systems of Wentzell equations and a description of the processing of the results of $n$ experiments at different values of a random variable having a standard normal distribution is given (confidence intervals according to the rule of three sigma are constructed for the obtained cross sections of the stochastic process describing quantitative changes in the geochemical regime of groundwater under non-pressure filtration and quantitative changes in free fluid filtration).
Keywords: stochastic filtration equation, stochastic free filtration equation, Wentzell system of equations, information processing, three sigma rule, Nelson – Glicklich derivative. 
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     title = {Information processing in a numerical study for some stochastic {Wentzell} systems of the hydrodynamic equations in a ball and on its boundary},
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N. S. Goncharov; G. A. Sviridyuk. Information processing in a numerical study for some stochastic Wentzell systems of the hydrodynamic equations in a ball and on its boundary. Journal of computational and engineering mathematics, Tome 11 (2024) no. 3, pp. 3-15. http://geodesic.mathdoc.fr/item/JCEM_2024_11_3_a0/