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.