A Note on Single-Step Difference Scheme for the Solution of Stochastic Differential Equation

Ashyralyev A. Okur U. Ashyralyyev C.
April 2024 Pleiades Publishing

Lobachevskii Journal of Mathematics
2024 #45 Issue 4 1366 - 1387 pp.

Abstract: This is a discuss on the application of operator approach to stochastic partial differential equations with dependent coefficients. Single step difference schemes generated by exact difference scheme for an abstract Cauchy problem for the solution of stochastic differential equation in a Hilbert space with the time-dependent positive operator are presented. The main theorems of the convergence of these difference schemes for the approximate solutions of the time-dependent abstract Cauchy problem for the parabolic equations are established. In applications, the convergence estimates for the solution of difference schemes for stochastic parabolic differential equations are obtained. Numerical results for the order of accuracy difference schemes of the approximate solution of mixed problems for stochastic parabolic equations with Dirichlet and Neumann conditions are provided. Numerical results are given.

a single-step difference schemes , stability , stochastic differential equations , well-posedness

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Department of Mathematics, Bahcesehir University, Istanbul, 34353, Turkey
Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Near East University Lefkoşa(Nicosia), Mersin 10, Turkey
Württembergische Gemeinde-Versicherungen, Stuttgart, 70164, Germany
Mirzo Ulugbek National University of Uzbekistan, Tashkent, 100174, Uzbekistan

Department of Mathematics
Peoples’ Friendship University of Russia (RUDN University)
Institute of Mathematics and Mathematical Modeling
Near East University Lefkoşa(Nicosia)
Württembergische Gemeinde-Versicherungen
Mirzo Ulugbek National University of Uzbekistan

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