Kunynets A. Three-point difference schemes of high order accuracy for stationary equations in cylindrical and spherical coordinate systems

The methods of Teylor series as well as Runge-Kutta method of the four order accuracy have been developed for the numerical solving the singular initial value problems for the nonlinear ordinary differential equations of the order 2. It has been constructed and justified the exact three-point difference scheme for solving the boundary problems of nonlinear stationary equations in the cylindrical and spherical coordinate systems on the non-uniform grid. An effective algorithmic realization of exact three-point difference scheme has been implemented via the truncated three-point difference schemes of arbitrary given accuracy order. The estimation of iteration method of serial approximation for the solving the nonlinear difference schemes has been obtained and the convergence of this method has been proved as well.