Numerical algorithm for finding a solution to a nonlinear filtration mathematical model with a random Showalter–Sidorov initial condition

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.