No abstract available

[en] A method for solving a system of nine-point differential equations approximating two-dimensional elliptical eqUations with mixed derivatives is described. The method is based on using the method of parabolic runs for solving a system of five-point equations. Results are presented of numerical investigations into the suggested method in model problems with Dirichlet and Neumann boundary conditions

[en] One of the schemes of the method of parabolic runs for solving two-dimensional elliptical differential equations is considered. The effectiveness of the scheme versus the value of iterative parameter introduced in it is illustrated in model problems. An effective method is suggested for solving the neumann problem for an equation of the heat conductivity type. It is shown experimentally that in case of variable coefficients of initial differential equations the effectiveness of the scheme considered weakly depends on the relation of the coefficient maximum value to the minimum one. A standard NFPP subprogram is described for solving two-dimensional differential elliptical equations using the method suggested

[en] In this paper a 3-level Chebyshev's algorithms for an acceleration of a convergence of external iterations in a solution of a stationary reactor problem on k eigenvalue and correspondent adjacent problem is developed. 8 refs

[en] The finite-difference schemes, which approximate two-dimensional reactor equation in case of one or several direct regions of the reactor boundary or zone boundary surface being non-parallel to the lines of coordinates, are plotted. For the solution of the obtained systems of the five-point equations h-factorization algorithm is used. The CONUS and CONCR programs for the calculation of the conical reactors without a reflector, and the CONOTR and CONCOL programs for the calculation of conical and conical-circular reactor systems with reflectors, are described. The obtained calculations have shown the working capacity of the built models and the effectivity of the used on the inner inerations of algorithm in comparison with other known methods

No abstract available

[en] An algorithm for calculating a reactor in the two-group diffusion approximation in (x,y)- and (r,z)-geometries is described. The difference equations satisfying the balance relationship are derived using the integral method. In order to find a solution of the five-point equations the internal iterative method is used that is a sort of the pertial factorization scheme. The scheme employed ensures a high convergence rate of the iterative process. The ''FACTOR'' computer code is written in the FORTRAN language for the ES-1030 computer and employs only the operative memory

[en] A new version of the incomplete factorization method for solving two-dimensional five-point elliptical-type difference equations is suggested. One of the method schemes is considered. It is shown experimentally that the combination of the scheme considered with h-factorization leads to considerable increase in the rate of convergence as compared with that for each of these schemes taken separately. It is shown that such combination of schemes possesses high efficiency when solving the Neuman problem for diffusion-type equation with a small diagonal predominance in the whole domain. The proposed method is applicable for solving a wide range of two- dimensional problems with the domains of arbitrary forms including calculation of critical parameters for nuclear reactors with complex configurations

[en] Algorithm of operative solution of the P₁-equation system of the method of spherical harmonics for cylindrical two-dimensial shield compositions has been developed and realized in the program. The algorithm is intended to be included into the system of program complex shield calculation according to techniques, combining succession application of discrete ordinate method and P₁-approximation. The algorithm is oriented to solution of the problems with preliminary axial radiation propagation at rather small gradients of solution with respect to radial variable. Difference analogues of P₁-equations were obtained under the assumption of exponential solution dependence on axial variable. The system of nonlinear finite-difference equations is solved with the use of effective technique, lying in successive application of h-factorization and parabolic runs. Independent algorithm testing, which demonstrated quick convergency of calculation process for a wide range of model problems, was conducted

[en] The paper presents an algorithm of partial factorization method (PFM) for solving a set of finite-difference equations for the reactor neutron-physical calculations in the hex-Z-geometry in the one-group diffusion approximations. The method of h-factorization efficiently suppressing smooth error components is used for the stationary problem. When calculating spatial kinetics in the prompt jump approximation there can be no conditions of diagonal predominance for the h-factorization use. In this case the PFM is used without any compensation of terms being iterated, and to accelerate the iteration process convergence the sequence of z-varied networks is applied. In each z-layer a seven-point operator is reversed according to the modified Zedan method. 7 refs.; 3 tabs