Issue N^{o} 1, 1988 
SOME GENERAL ASPECTS OF ALGORITHM DEVELOPMENT FOR CONSTRUCTING DIFFERENCE GRIDS
G. P. Prokopov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 313.
The paper examines some issues related to designing algorithms for regular difference grid construction with systems of el 1iptictype differential equations. Making the associated mapping univalent in the case of complicatedshape region is an extremely difficult problem. Achieving a sufficient mapping flexibility requires that governing functions should be introduced into the equations used. Nonuniform rectangular and polar grids are used to study advantages and disadvantages of various algorithms.

HE RAPID TECHNIQUE FOR COMPUTING 2D ADIABATIC FLOWS IN COMPRESSIBLE MEDIA USING LAGRANGIAN VARIABLES WITH FREE POINT NEIGHBORHOOD T. N. Alekseeva, V. A. Bychenkov, V. F. Kuropatenko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 1421.
A 2D difference method is presented for calculating fluid and elasticplastic flows in Lagrangian coordinates. The method relies upon principles of free points neighborhood. The conservation laws are integrated using Dirichlet cells constructed for these points. The difference scheme is explicit. The continuity difference equation approximates the mass conservation law in a differential form and is adapted to the solution at each timestep. A numerical example for the Schultz problem is given.

METHODS FOR SOLVING 3D GAS DYNAMICS EQUATIONS IN MIXED LAGRANGIANEULERIAN COORDINATES V. V. Zmushko, F. A. Pletenev, V.A.Saraev, I. D. Sofronov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 2227.
Numerical calculation of 3D equations in gas dynamics is examined. Equations are derived for mixed coordinates where some coordinate lines are Lagrangian and others are Eulerian. A difference scheme is given for a particular coordinate system with two Lagrangian and one Eulerian directions which was obtained from an original Cartesian system. Numerical results of 3D perturbation evolution calculations are discussed for the RayieighTaylor instabiIity.

PARAMETER ESTIMATION IN A TWO  PARAMETER LINEAR REGRESSION DEPENDENCE USING THE THEIL METHOD A. M. Khotinsky VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 2837.
A Theil method generalization is proposed and studied for obtaining stable parameter estimators in a twoparameter linear regression dependence. The estimators are proved to be asymptotically unbiased and normal. An approach to generate confidence intervals is justified. This approach is shown to be suitable for exponential dependence analyses.

A WAY TO INCREASE SOLUTION ACCURACY FOR DIFFERENCE SCHEMES CONSTRUCTED WITH THE GODUNOV METHOD N. Ya. Moiseev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 3845.
A modified Godunov scheme is derived which has a thirdorder approximation for linear and acoustic equations with fixed coefficients and one, two, and three spatial variables. The scheme approximation is studied for spatial grids with fixed timesteps along the coordinate lines. The paper provides further improving the Godunov scheme modification method which has been adressed by the author. Results for test problems with exact solutions are reported.

THE IP METHOD FOR SOLVING 1D NONEQUILIBRIUM RADIATION TRANSPORT PROBLEMS Yu. K. Kochubey VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 4656.
A method for solving 1D nonequilibrium radiation transport problems is considered. A Vladimirov1ike transport equation is approximated with a threepoint difference scheme. An iterative method is proposed for solving transport, energy balance, and level population kinetics equations. The method efficiency is illustrated by numerical calculations.

EXISTENCE AND UNIQUENESS OF KINETIC EQUATION SOLUTIONS FOR QUASIPARTICLES IN NONEQUILIBRIUM SUPERCONDUCTORS B. N. Shamraev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 5760.
The solution of a stationary spaceuniform kinetics equation is proved to exist and to be unique for quasiparticles in nonequilibrium superconductors. The case of a broad quasiparticle source and equilibrium Zerotemperature phonon distributions is examined. An efficient numerical algorithm for finding a solution is described.

EXISTENCE AND UNIQUENESS OF A KINETIC EQUATION FOR QUASI PARTICLES IN SUPERCONDUCTORS WITH EQUILIBRIUM PHONONS A. S. Sukhikh VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 6164.
The paper presents a proof of existence and uniqueness of a spaceuniform timeindependent kinetic equation for quasiparticles in nonequilibrium superconductors. Newton method is proved to converge for this equation.

A PACKAGE FOR COMPUTING GAS DYNAMIC FLOWS IN VARIABLE CROSSSECTION TUBES Yu. N. Deryugin, I. F. Kazakova, М. M. Proshin, L. I. Sizova, B. P. Tikhomirov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 6569.
We describe a package designed to solve numerically 1D nonstationary problems in gas dynamics involved in nonuniform flow studies within variable crosssection tubes with jumps and perforated membranes. The calculations are performed in moving coordinates by explicitely locating the jumps and calculating through shock waves. Integrating the main equations uses the Godunov, LaxWendroff, McCormack schemes and a modified Godunov method. The package capabilities are exemplified by six problems.

D NONSTANTIONARY CONTINUUM MECHANICS PROBLEM CONTROL IN THE INTEGRATED SIGMA PACKAGE RUNNING IN PARALLEL ON THE ELBRUS MULTIPROCESSOR Yu. G. Bartenev, I. V. Demin, A. I. Lukin, V. A. Saraev, I. D. Sofronov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 7074.
Vie examine the implementation of a parallel scheme for computations on the Elbrus multiprocessor using the Sigma Package. The multiprocessor SVS OS capabilities are extensively exploited. These include events sequencing, parent and offspring tasking, shared main and drum memory.

EFFICIENT CROSSSECTIONS OF PHOTON INTERACTION WITH A NOHOMOGENEOUS ABSORB ING MEDIUM F. M. Shmakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 1. P. 7579.
A scheme is proposed for a statistical description of the radiation interaction with a nonhomogeneous medium. The sample being examined is splitted into N layers of thickness L in such a manner that interinclusion screening may be neglected. Assuming the inclusions to be uniformly and independently spaced we obtain a throughpath length propability distribution density for an inclusion in one layer. This allows to evaluate the integrated throughpath length probability distribution densities for N layers and use these in order to derive expressions for computing efficient crosssections for materials with various inclusions (spheres, cubes, and lines). Conditions for limit transition to a homogeneous medium are considered.

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