A numerical evaluation of the Liouville-Green approximation of variable-coefficient Lanchester-type equations of modern warfare

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Author
Carpenter, James N.
Date
1976-03Advisor
Taylor, J.G.
Second Reader
Brown, Gerald G.
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Show full item recordAbstract
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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