Rubric: "01.01.05 Probability theory and mathematical statistics"

doi: 10.18698/2309-3684-2017-2-107123

We used the theory of continuous-time Markov processes as the basis for developing our stochastic “mixed” models of reciprocal hostilities and a numerical algorithm that makes it possible to compute main combat metrics for large forces. We show that a pre-emptive strike performed by one of the belligerents significantly affects the outcome and main metrics of combat between forces that are sufficiently similar in strength. We determine that it is not the initial numerical strengths of the two belligerents but their balance of power that affects errors shown by the method of dynamics of mean values; moreover, the errors increase with increasing the time to a pre-emptive strike.

Chuev V. Yu., Dubogray I.V. “Mixed” stochastic models of reciprocal hostilities for the case of one belligerent performing a pre-emptive strike. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 107-123

doi: 10.18698/2309-3684-2017-2-94106

We conducted a numerical experiment in applying the shooting method to solve problems of optimal control with switching. We used the problem of lunar soft-landing to test an algorithm that ensures convergence of Newton's method in problems of this type. We analysed the accuracy of our computations.

Mozzhorina T. Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 94-106