THE USE OF MODIFIED EQUATION OF DYNAMICS OF MEDIUM FOR OPERATIVE FORECASTING OF THE COURCE AND RESULTS OF THE COMBAT ACTIONS

Abstract

The article is devoted to the consideration of the peculiarities of the use of equations of dynamic of the medium for the operational forecasting of the course and the results of combat operations. Different topologies of the equations of Lancaster can be used as a tool for predictive calculations, taking into account the efficiency of obtaining results and the clear physical content of the components of such equations. But, to the important limitations of the models of dynamics of medium should include assumptions about the homogeneity of the staff of the opposing groups. The heterogeneity of the staff of the groups, as well as the variable intensity of the receipt of reserves to the groups during combat operations, can be taken into account by varying the corresponding coefficients in the complex systems of equations. The use of variable coefficients in systems of differential equations in the course of their numerical integration requires an evaluation of the stability of the solutions obtained by Liapunov. Preservation of the efficiency of the implementation of predictive calculations based on modified equations of Lancaster is possible with the use of modern simulation environments with the numerical integration algorithms implemented in them. The article gives an example of an analytical solution of the system of the Lancaster equations with the estimation of the stability of the solution for constant coefficients, as well as the results of the solution of the same system by a numerical method in the AnyLogic environment for constant and variable coefficients of the intensity of replenishment of the grouping. The confirmed convergence of the results allowed us to suggest the use of the modification of the systems of the equations of Lancaster with variable coefficients with the simultaneous assessment of the stability of their solutions to approximate this description to the realities of combat operations and increase the reliability of the results.

Keywords

• dynamics method of medium
• equation of lancaster
• the dynamics of combat actions