scholarly journals Modeling and forecasting the probability of the states of technical support systems for the use of weapons and military equipment

Author(s):  
A. Ugol’nikov ◽  
B. Demianchuk ◽  
S. Shelukhin ◽  
O. Malynovskyi ◽  
A. Kosenko

The article discusses a probabilistic model of processes in complex systems of technical support for military vehicles. One of the methods for studying such complex systems is their representation in the form of a set of typical states in which the system can be. Transitions occur between states, the intensities and probabilities of which are assumed to be known. The system is graphically represented using a graph of states and transitions, and the subject of research is the probability of finding the technical support system in these states. The graph of states and transitions is associated with a system of first order linear differential equations with respect to the probabilities of finding the support system in its basic states. To obtain a solution, this system must be supplemented with certain conditions. These are, firstly, the initial conditions that specify the probabilities of all states at the initial moment of time. Second, this is the normalization condition, which states that at any moment in time the sum of the probabilities of all states is equal to unity. An approximate solution to the problem is described in the literature. Such approximate solution is getting more accurate when the sought probabilities depend on time weaker. We propose a method of the exact solution of the above mentioned system of differential equations based on the use of operational calculus. In this case, the system of linear differential equations is transformed into a system of linear algebraic equations for the Laplace images of unknown probabilities. The use of matrix calculus made it possible to write down the obtained results in a compact form and to use effective numerical algorithms of linear algebra for further calculations. The model is illustrated by the example of solving the problem of technical support for the march of a battalion tactical group column, including wheeled and tracked vehicles. The boundaries of the validity of the results of a simpler approximate solution are established.

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.


Author(s):  
Юрий Иванович Скалько ◽  
Yu I Skalko ◽  
Сергей Юрьевич Гриднев ◽  
S Yu Gridnev

We construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with constant coefficients. We propose an algorithm for an approximate solution of the generalized Riemann problem on the breakup of a discontinuity under additional conditions at the boundaries, which allows one to reduce the problem of finding the values of variables on both sides of the discontinuity surface of the initial data to the solution of a system of algebraic equations. We construct a computational algorithm for an approximate solution of the initial-boundary-value problem for a hyperbolic system of first-order linear differential equations. The algorithm is implemented for a system of equations of elastic dynamics; it is used for solving some applied problems associated with oil production.


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