Combat modeling with partial differential equations

Protopopescu, V.; Santoro, R.T.; Dockery, Jack D.

doi:10.1016/0377-2217(89)90102-1

Cited by 28 publications

(13 citation statements)

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“…Since then, his model has been refined and exercised in great detail. The Lanchester model has been constructed as stochastic differential equations by Morse [10], in mixed form by Deitchman [4], in matrices by Maybee [9], and as partial differential equations using explicit spatial variable by Protopopescu, Santoro, and Dockery [11]. Taylor [13] has even published a two-volume book on the mathematical analysis of Lanchester's equations.…”

Section: Introductionmentioning

confidence: 99%

Applying Lanchester's linear law to model the Ardennes campaign

Chen

Chu

2001

Naval Research Logistics

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Abstract:In modern warfare, many believe the decisive factor in winning a battle is seizing the right moment to shift from defense to attack, or vice versa. This paper attempts to bring that perspective to Lanchester's differential equations of warfare, and continues the application of Lanchester's linear law to the analysis of the World War II battle of Ardennes, as reported in earlier issues of Naval Research Logistics by Bracken and by Fricker. A new variable, shift time, accounting for the timing of the shift between defense and attack is explicitly included in our version of the model, and it helps obtain improved goodness of fit to historical data.

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Section: Introductionmentioning

confidence: 99%

Applying Lanchester's linear law to model the Ardennes campaign

Chen

Chu

2001

Naval Research Logistics

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“…In [45] the kernels k u , k v were of the form βe −ν i |x−y| so that the efficacy increases with decreasing distance with a maximum value at zero as expected for say, a rifle.…”

Section: Protopopescu Et Almentioning

confidence: 96%

“…Progress has been made by Protopopescu et al [45,46], Rusu [47] and Jaiswal [20], addressing some of the major criticisms of the ODEs and reflecting the development in numerical techniques and computational ability of the 1980s and 1990s.…”

Section: Introductionmentioning

confidence: 99%

Combat modelling with partial differential equations

Keane

2011

Applied Mathematical Modelling

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“…5 where with the initial conditions given by the spatial functions A combat model interpretation of the terms appearing in the equations has been given in Ref. 5 and is briefly recalled here for the reader's convenience. The diffusion terms express the natural tendency of any force, ancient or modern, to lose its initial configuration as it moves, fights, etc., or simply just as time goes by, due to fatigue, loss of concentration, loss of motivation, etc.…”

Section: Fuzzy Lanchester Equationsmentioning

confidence: 99%

“…For a particular set a , h, a ' , b', and for a particular function form for c(x), ~'(x), e(x), and g(x), we can get a solution for u and u via the computer model discussed in Ref. 5. Thus, we can denote this as…”

Section: Fuzzy Lanchester Equationsmentioning

confidence: 99%

Combat modeling with imprecise data

Protopopescu

Yager

Dockery

1992

Int. J. Intell. Syst.

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We apply the fuzzy description to some analytic models of combat; based on ordinary differential equations. The extension to a more involved partial differential equations model is briefly mentioned. The merits of the fuzzy description versus the deterministic or probabilistic descriptions are discussed. I. BACKGROUNDThe function of command and control (C2) is to direct combat. It does so by imposing a pattern and a purpose on what otherwise would appear as deadly chaos. With C2 in operation, encounters are no less deadly but some long range order may appear from the chaos. C2 works prospectively and retrospectively through the planning function. This may be thought of as a feedforward procedure. In between it attempts to function in something approaching real time appropriate to its distance from the actual combat. In this instance C2 is following feedback procedures.Whether the results of the combat bode good or ill depends on the execution of the aforementioned feedforward and feedback procedures. The formulation and execution of these procedures depends in part on information flow. When the data are imprecise, the planning is more and more generic and driven by the necessity of allowing for a wide variety of contingencies. Similarly, the

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Combat modeling with partial differential equations

Cited by 28 publications

References 0 publications

Applying Lanchester's linear law to model the Ardennes campaign

Applying Lanchester's linear law to model the Ardennes campaign

Combat modelling with partial differential equations

Combat modeling with imprecise data

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