Lanchester’s equations in three dimensions

This paper generalizes Lanchester’s equations of warfare to partial differential equations involving time and two spatial variables. Unlike in Lanchester’s original ordinary differential equations, the distribution of armies over the battlefield must be considered. Four different modes of attack are...

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Veröffentlicht in:	Computers & mathematics with applications (1987) 2007-04, Vol.53 (7), p.999-1011
Hauptverfasser:	Spradlin, Christina, Spradlin, Greg
Format:	Artikel
Sprache:	eng
Schlagworte:	Area fire Battlefield simulation Computer simulation Differential equations Direct fire Fires Lanchester’s equations Mathematical analysis Mathematical models Reaction–diffusion equations Stress concentration Three dimensional Warfare
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description	This paper generalizes Lanchester’s equations of warfare to partial differential equations involving time and two spatial variables. Unlike in Lanchester’s original ordinary differential equations, the distribution of armies over the battlefield must be considered. Four different modes of attack are introduced, generalizing Lanchester’s equations for area fire and for direct fire. The effect of the distribution of forces and their movement on the outcome is considered, and numerical simulations given.
doi_str_mv	10.1016/j.camwa.2007.01.013
format	Article
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subjects	Area fire Battlefield simulation Computer simulation Differential equations Direct fire Fires Lanchester’s equations Mathematical analysis Mathematical models Reaction–diffusion equations Stress concentration Three dimensional Warfare
title	Lanchester’s equations in three dimensions
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