Combat modeling with partial differential equations
A new analytic model based on coupled nonlinear partial differential equations is proposed to describe the temporal and spatial evolution of opposing forces in combat. Analytic descriptions of combat have been developed previously using relatively simpler models based on ordinary differential equations (.e.g, Lanchester's equations of combat) that capture only the global temporal variation of the forces, but not their spatial movement (advance, retreat, flanking maneuver, etc.). The rationale for analytic models and, particularly, the motivation for the present model are reviewed. A detailed description of this model in terms of the mathematical equations together with the possible and plausible military interpretation are presented. Numerical solutions of the nonlinear differential equation model for a large variety of parameters (battlefield length, initial force ratios, initial spatial distribution of forces, boundary conditions, type of interaction, etc.) are implemented. The computational methods and computer programs are described and the results are given in tabular and graphic form. Where possible, the results are compared with the predictions given by the traditional Lanchester equations. Finally, a PC program is described that uses data downloaded from the mainframe computer for rapid analysis of the various combat scenarios. 11 refs., 10 figs., 5 tabs.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 5639191
- Report Number(s):
- ORNL/TM-10636; ON: DE88004764
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990230* -- Mathematics & Mathematical Models-- (1987-1989)
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
KINETIC EQUATIONS
MATHEMATICAL MODELS
MILITARY STRATEGY
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
WARFARE