Geodesic
Numerical algorithm for finding a solution to a nonlinear filtration mathematical model with a random Showalter--Sidorov initial condition
Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 39-51.

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The article is devoted to the study of a nonlinear model of fluid filtration based on the stochastic Oskolkov equation. It is assumed that the experimental initial data is affected by "noise", which leads to the study of a stochastic model with the Nelson–Glicklich derivative. Sufficient conditions for the existence of solutions of the investigated model with the initial Showalter-Sidorov condition are constructed. An algorithm for the numerical solution method is constructed and a computational experiment is presented.
Keywords: Sobolev type equations, stochastic model of nonlinear filtration, Nelson–Glicklich derivative. 
@article{JCEM_2022_9_2_a3,
     author = {K. V. Perevozchikova and N. A. Manakova and O. V. Gavrilova and I. M. Manakov},
     title = {Numerical algorithm for finding a solution to a nonlinear filtration mathematical model with a random {Showalter--Sidorov} initial condition},
     journal = {Journal of computational and engineering mathematics},
     pages = {39--51},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2022_9_2_a3/}
}
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K. V. Perevozchikova; N. A. Manakova; O. V. Gavrilova; I. M. Manakov. Numerical algorithm for finding a solution to a nonlinear filtration mathematical model with a random Showalter--Sidorov initial condition. Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 39-51. http://geodesic.mathdoc.fr/item/JCEM_2022_9_2_a3/