A numerical evaluation of the Liouville-Green approximation of variable-coefficient Lanchester-type equations of modern warfare
Carpenter, James N.
Brown, Gerald G.
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This thesis evaluates the so-called Liouville-Green approximation to the solution of variable-coefficient Lanchester-type equations for combat between two homogeneous forces. When compared to the form of the exact solutions, this approximation is in terms of "elementary" functions. Two specific forms of attrition-rate coefficients are considered, allowing for different maximum effective ranges of the two opposing weapon systems. These coefficients might be used to model a constant-speed attack against a static defensive position. It is shown that for these attrition-rate coefficients, the Liouville-Green approximation is not consistently reliable for predicting force levels, and yields exact results only under certain restrictive conditions. ' Furthermore it was found that methodology is not presently available to accurately predict from Liouville's normal form the error which will be incurred by invoking the approximation in a specific situation.
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On Liouville's normal form for Lanchester-type equations of modern warfare with variable coefficients Taylor, James G. (Monterey, California. Naval Postgraduate School, 1978-09); NPS55-78-024This paper shows that much new information about the dynamics of combat between two homogeneous forces modelled by Lanchester-type equations of modern warfare (also frequently referred to as 'square-law' attrition equations) ...
Taylor, James G. (Monterey, California. Naval Postgraduate School, 1977-06); NPS55-77-29New error bounds are developed for the Liouville-Green approximation to the solution of an important class of differential equations arising in military operations research (specifically, variable-coefficient Lanchester-type ...
Phillips, Michael D. (Monterey, California. Naval Postgraduate School, 1991-06);The purpose of this thesis is to investigate and establish Sturm- Liouville properties for special eigenfunctions which are expressed in determinant form. In particular, a special case is presented where the elements of ...