Елементи імітації у рівняннях моделей ланчестерського типу

Abstract

The article gives a brief overview of the possible scope of application of modifications of the Lanchester type models, and also considers some features of the use of simulation elements and numerical solution of differential equations of such models in stochastic formulation. The interest to the models of the Lanchester type, which is traced by the publications in the thematic periodicals, testifies to the effectiveness of such apparatus for solving the problems of operational forecasting of changes in the number of opposing groups during the combat operations. Stochastic formulation allows to simulate in a certain way the influence of random factors and to take into account the elements of uncertainty that influence the dynamics of changes in the number of opposing factions, and which to some extent are present in any combat operations. In contrast to deterministic models, stochastic models require the use of special numerical methods, the choice of a particular model can be justified by the requirements for the degree of their convergence on the integration interval. Evaluation of the convergence can also serve to verify the correctness of the software implementation of the selected method. The article considers a comparative example of using the Milstein method for numerical solution of the Lanchester model differential equations in stochastic formulation.