Article

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

Allaberen AshyralyevPeoples’ Friendship University of Russia (RUDN University), 117198, Moscow, RussiaÜlker OkurNear East University Lefkoşa (Nicosia), Mersin 10, TurkeyCharyyar AshyralyyevDepartment of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey

Computational Mathematics and Mathematical Physicsjournal2025en

ABI

Abstract

In the present paper, the single step Crank–Nicolson difference scheme of the $$3{\text{/}}2$$ 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 $$3{\text{/}}2$$ 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.

Topics

Differential Equations and Boundary Problems Stochastic processes and financial applications Differential Equations and Numerical Methods

Identifiers

DOI: 10.1134/s096554252570143x

Citations and references

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