Issue N^{o} 2, 1987 
APPLICATION OF VARIATIONAL PRINCIPLES OF MECHANICS TO DEVELOPING TIMEDISCRETE DIFFERENCE GAS DYNAMICS MODELS. 3. NONUNIFORM DIFFERENCE SCHEMES WITH VARIOUS TIMESTEPS IN NEIGHBOURING CELLS
Yu. A. Bondarenko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 310.
Using finitedimensional approximation of the Hami1tonOstrogradski functional on spacetime irregular difference meshes the conservative variational difference schemes are derived allowing calculation of gas dynamics problems on arbitrary Lagrangian meshes with neighbouringcell time steps which differ twice from one another. In subregions of the same timesteps in all the cells the derived difference schemes are equivalent to variational difference schemes of the "KREST" type. The numerical test results indicate that with the fixed neighbouring cell timestep ratio the additional error due to nonuniformity of the difference schemes proposed is small as compared to approximation errors of the standard difference scheme "KREST".

SOME PROBLEMS CONCERNING FULLY CONSERVATIVE DIFFERENCE SCHEMES FOR COMPUTING TWODIMENTIONAL AXI SYMMETRIC GAS DYNAMICS FLOWS S. M. Bakhrakh, V. F. Spiridonov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 1119.
Analytical fullenergy disbalance estimates are obtained which are associated with various means of derivation of operator "grad" in difference schemes which is invariant relatively to three types of flow symmetry (plane, cylindrical, spherical). The effect of the time and space disagreement of difference schemes on energetic disbalance quantity in the numerical solution, as well as associated accuracy decrease, are illustrated by two test problems, the solution of one of which has been obtained by the authors.

CUBIC SPLINE INTERPOLATION A. S. Shvedov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 2022.
A problem of deriving the cubic spline s ∈ c^{i} [a,b] assuming given values in given (support) points of the segment [a,b]. The problem is simple but very important for applications. A new way of deriving such splines is suggested which possesses the following properties. Firstly, the splines are monotonic between any two neigbouring support points. Secondly, the first and second spline derivatives (the latter are discontinuous in general) are upperbounded by associated separated differences derived by support points and spline values at those points.

AN IMPLICIT INHOMOGENEOUS METHOD OF SOLVING QUASILINEAR TRANSFER EQUATION. INTERACTION OF DISCONTINUITIES N. N. Bokov, Z. G. Glinskikh VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 2328.
For an Implicit inhomogeneous method of solving quasi linear transfer equation questions are considered which arise at:  interaction of discontinuities;  sharp discontinuity formation in solution due to incorrect initial data and boundary conditions;  Riemann problem. Algorithm of interaction of steady discontinuities, Riemann problem, and "check points" method are suggested for defining place and moment of creation of sharp discontinuity from continuous initial data and boundary conditions. These algorithms use the method’s property to retain weak discontinuities in solution. Convergence of the difference solution to the exact one is demonstrated by numerical calculations.

STABILITY OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS IN ARBITRARY NORMS N. Yu. Bakayev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 2934.
A number of questions associated with examining stability of difference schemes in arbitrary Banach space is considered. In particular, the property of retaining the scheme stability property is examined with disturbings of the problem operator, and the role of smoothing operators is determined Difference schemes for differential equations with operators of a wide (in the sense of practical application) class are discussed as appendices in the рареr.

NUMERICAL ALGORITHM AND PROGRAM FOR GROUP ACCUMULATION EFFECTS CALCULATION V. A. Sholokhova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 3544.
A brief description of numerical algorithm of kinetic equation solution, of computational program capabilities, and obtained results on dose accumulation factors and accumulation factors of absorbed energy from point and plane isotropic radiation sources is given. The numerical solution results are tabulated. The tables include group data for seven energetic groups of gamma quanta over the 010 MeV range obtained by FORTRAN code on BESM6 computer. Various media are studied.

A CODE FOR DERIVING ELECTRON TRAJECTORIES BY THE MONTECARLO METHOD IN INFINITE HOMOGENEOUS MEDIUM E. N. Donskoy, N. Y. Ivanov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 4556.
The algorithm is described and the code ELTR for modelling electron trajectories in infinite homogeneous medium by the MonteCarlo method is presented. The algorithm is based on FockerPIank approximation for glancing collisions. The algorithm differs from existing ones mainly in that its realization does not need preliminary tabulating any distributions. Comparative computational results are given confirming efficiency of the code ELTR.

ON TWO METHODS OF SOLVING EIGEN VALUE PROBLEM FOR A SET OF SECONDORDER DIFFERENTIAL EQUATIONS OF THE MULTIDIMENSIONAL ANGULAR COULUMB FUNCTIONS METHOD A. I. Golubev, V. M. Povyshev, A. A. Sadovoy, M. K. Sarayeva VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 5763.
Two numerical methods are proposed for solving eigen/value problem for a set of secondorder ordinary differential equations arising when the method of multidimensional angular Coulomb functions is used in multielectron atom theory. In Galerkin method using all particular solution limitations the solution of lower eigen/values is reduced to nonlinear algebraic equation solution. In the Sturm distribution method a set of linear algebraic equations is solved numerically to derive eigen/values and eigen vectors. Numerical results are supplied illustrating convergence of both methods.

MULTI SEQUENCING OF APPLICATIONS ON OS SVS O. A. Abramova, Yu. G. Bartenev, V. A. Erzunov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 6470.
New means (extracodes and task descriptor parts) of OS SVS are described allowing most comprehensive use of capabilities of multiprocessor complex of backend processors MVK "Elbrus1" (SVS) for computing applications. New means of multi sequencing of applications allow to considerably enhance address space, to present the application as asynchronous processes, to control their execution and to realize their interaction on the basis of semaphores and events.

SOFTWARE ARCHITECTURE OF LOCAL AREA NETWORK N. N. Zalyalov, A. L. Lukyanov, V. A. Skotnikov, S. K. Khlystov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 7178.
Net software architecture is described which is designed for constructing distributed automatized systems. Software support provides twopoint connection in twolevel hierarchical configuration of network consisting of SM4 type minicomputer and "Electronika60" type microcomputer and permits the following: teieloading, telecommunication, and teleaccess. Software support is made for operating system OSRV, MOSRV, RAFOS, for QUEYSIC programming system, and for RAMresident versions of network application programs. Support for OSRV and MOSRV provides operation at all data transfer facilities served by terminal driver. In addition, provision is made for using data transfer facilities controlled by joboriented drivers. Each support allows simultaneous run with several data transfer facilities.

DATAWAY CONSOLE PROTOCOL N. N. Zalyalov, S. F. Khlystov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 7985.
Dataway console protocol is described as a component of hierarchy of logs of network distributed processing software package. It is a byteoriented balanced protocol using both a terminal handler for controlling physical communication channel and a joboriented handler for controlling single and multichannel data transfer facilities. The protocol provides twopoint connection in twolevel hierarchy network configuration, including SM4 type minicomputer and "Electronika60" type microcomputer. Software support of the protocol is made for various operational media, such as OSRV, MOSRV, RAFOS, QUEYS1K programming system, and for RAMresident variant. Each support allows simultaneous service of several transfer facilities.

PROBABILITY DENSITY ASSESSMENT BY A FINITE SET OF INTEGRAL DATA M. Z. Tarasko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 2. P. 8691.
The problem of assessment of probability density of a physical quantity by a finite set of integral experimental data is posed as a problem of assessing distribution parameters of maximum entropy exponetial family. The algorithm and the standard routine of parameter optimization are described.

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