AN INTEGRATED CLASS ON MATHEMATICAL MODELING OF A MARKOV PROCESS USING THE LANCHESTER MODEL AND ITS SOLUTION IN MATLAB
DOI:
https://doi.org/10.31110/fmo2024.v39i5-01Keywords:
stochastic modelling, Lanchester model, state-transition diagram, Kolmogorov equations, MATLAB, teachingAbstract
Formulation of the problem. The development of skills in applying classical mathematical tools to solve real problems is one of the tasks of mathematical disciplines in higher education. It requires a constant replenishment of the base of modern applied problems. A significant portion of these problems do not have “elegant” solutions and require the use of software. This creates the challenge of integrating the theoretical mathematical foundation, practical application, and the use of information technology. To address this, it is advisable to conduct integrated classes that include mathematics, the speciality, and computer science.
Materials and methods. To conduct the research, a stochastic approach to mathematical modelling of combat was used (a state-transition rate diagrams of a Markov process with specified transition intensities, a system of Kolmogorov differential equations). Programs were created in the MATLAB system using built-in functions for solving differential equations with initial conditions and for finding function limits.
Results. The paper presents the integrated class on mathematical modelling of the "highly organized" Lanchester battle with professional course. The solution of the problem by a stochastic approach for initial values in the simplest case is described in detail. Recommendations are presented for cadets (students) to independently build a solution algorithm in MATLAB for more complex cases.
Conclusions. Conducting an integrated lesson increases the interest of cadets in studying mathematics and applying its tools in professional activities. A detailed description of the solution of the Lanchester model considered in the work can be used to build and solve similar stochastic models in military affairs, economics, engineering, etc. The paper presents a description of an integrated class on combat modelling, which can be implemented in the study of “Probability Theory”, “Theory of Random Processes”, and “Queueing Systems”.
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Vira, M., & Samusenko, P. (2024). Rozv’yazannya zadach liniynoho prohramuvannya iz zastosuvannyam prohramnoho zasobu Geogebra. [Solving linear programming problems using the Geogebra software tool]. Physical and mathematical education, 39(1), 14–20. (in Ukrainian).
Mykhalevych, V.M. (2004). Maple. Komp’yuterna pidtrymka kursu vyshchoyi matematyky v tekhnichnomu vuzi. [Maple. Computer support for the course of higher mathematics in a technical university]. VNTU. (in Ukrainian).
Spivakovsʹkyy, O. V. (2003). Teoriya i praktyka vykorystannya informatsiynykh tekhnolohiy u protsesi pidhotovky studentiv matematychnykh spetsialʹnostey. [Theory and practice of using information technologies in the process of training students of mathematical specialties]. Aylant. (in Ukrainian).
Fursenko, O., Chernovol, N., & Bobrytsʹka, H. (2024). Matematychni modeli boyovykh diy yak zasib vdoskonalennya profesiynoyi oriyentovanosti vykladannya matematychnykh dystsyplin u VVNZ. [Mathematical models of combat operations as a means of improving the professional orientation of teaching mathematical disciplines in military universities]. Physical and mathematical education, 39(1), 64–69. https://doi.org/10.31110/fmo2024.v39i1-09. (in Ukrainian).
Khalanchuk, L. V. (2021) Zastosuvannya paketu MathCAD na laboratornykh zanyattyakh z vyshchoyi matematyky. [Application of the MathCAD package in laboratory classes in higher mathematics]. Materials of the 2nd All-Ukrainian scientific and methodical internet conference of students, postgraduates and young scientists "Development of intellectual skills and creative abilities of pupils and students in the process of learning the disciplines of the science and mathematics cycle "ITM*plus-2021" Forum of young researchers", November 12, 2021. (pp. 149-150). Sumy. (in Ukrainian).
Armstrong, M.J. (2011). A verification study of the stochastic salvo combat model. Annals of Operations Research, 186, 23-38.
Schaffer, M.B. (1968). Lanchester models of guerrilla engagements. Operations Research, 16(3), 457-488.
Thomas, W.L. (2000). The Stochastic Versus Deterministic Argument for Combat Simulations: Tales of When the Average Won't Do. Military Operations Research, 5(3), 9-28.
Vesa, K. (2015) A Combat Equation Derived from Stochastic Modeling of Attrition Data. Military Operations Research, 20(3), 49-69.
Wang, J. (2024) The Application of MATLAB in the Mathematics Teaching of Computer Majors. Scalable Computing: Practice and Experience, 25(4). https://doi.org/10.12694/scpe.v25i4.2889
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