Iranian Journal of Wargaming

Iranian Journal of Wargaming

Land wargame simulation using fractional order Lanchester differential equations

Document Type : Original Article

Authors
Nader Biranvand 1
Hamid Bigdeli 2
Mohammad Taghi Partovi 3
Amir Hosein Hadian Rasanan 4
1 Assistant Professor, Imam Ali Officer University. Tehran, Iran.
2 Department of science and technology studies, AJA Command and Staff University. Tehran, Iran.
3 Assistant Professor,AJA Command and Staff University. Tehran.Iran.
4 Researcher, Institute for Research in Fundamental Sciences (IPM),Tehran.Iran.
10.22034/ijwg.2023.352339.1027
Abstract
Lanchester equations are frequently applied in simulating wargames and modeling the population dynamics of combat forces of groups involved in operational areas. These equations can provide an estimate of the population of the two groups in the future and determine the victorious force of the war by considering factors such as the casualty rate of internal forces and enemy forces. However, all the calculations performed in these models are done according to the momentary changes in population dynamics. While the events that happened in the past can be effective in determining the future status of the forces. For this purpose, in this article, we intend to add the memory mechanism in the Lanchester equations by using fractional derivatives and analyzing it from a military perspective. Then, by applying a fractional multistep scheme, we will simulate these equations. Finally, by presenting some examples, we will examine and study the behavior of the proposed fractional Lanchester equations. The numerical scheme used in this paper is an Adams-Moulton-Bashforth fractional multistep scheme for Caputo sense fractional derivatives, which can simulate differential equation problems with high stability and accuracy. The results obtained in this paper show that by reducing the order of the derivative in the Lanchester equations and using memory in the model, the loss rate increase compared to the normal models.
Keywords
Lanchester equations
Fractional calculus
Caputo derivative
Multi-step methods
Numerical simulations
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