A Note on the Crank–Nicolson Difference Scheme for the Numerical Solution of Stochastic Parabolic Equation

Ashyralyev A. Okur U. Ashyralyyev C.
November 2025 Pleiades Publishing

Computational Mathematics and Mathematical Physics
2025 #65 Issue 11 2528 - 2545 pp.

Abstract: In the present paper, the single step Crank–Nicolson difference scheme of the th order of accuracy for the numerical solution of the Cauchy problem for the parabolic equation with dependent operator is considered. Theorems on the stability and the convergence of this difference scheme are established. In application, the convergence estimates for the solution of difference scheme for stochastic multidimensional parabolic differential equation are proved. Numerical results for the th order of accuracy difference scheme of the approximate solution of mixed problems for 1D and 2D stochastic parabolic equations with Dirichlet condition are provided.

convergence , Crank–Nicolson difference scheme , parabolic equation with dependent operator , stability , stochastic parabolic equation

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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
Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, 160200, Kazakhstan
National University of Uzbekistan named after Mirzo Ulugbek, 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
Khoja Akhmet Yassawi International Kazakh-Turkish University
National University of Uzbekistan named after Mirzo Ulugbek

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