Research of convergence of the iterative method for solution of the Cauchy problem for the Navier - Stokes equations based on estimated formula

Abstract

Solution of the Navier-Stokes equations with initial conditions (Cauchy problem) for 2D and 3D cases was obtained in the convergence series form by iterative method using Fourier and Laplace transforms in paper $\cite{TT02}$. For several combinations of problem parameters numerical results were obtained and presented as graphs. Estimated formula for the border of the parameter area of convergence of the iterative method was obtained in paper $\cite{TT03}$. This paper describes numerical proof of convergence of the iterative method for solution of the Cauchy problem for the Navier - Stokes equations. Usage of estimated formula for the border of the parameter area of convergence of the iterative method is shown for wide ranges of the problem's parameters.