A Numerical Evaluation of the Liouville-Green Approximation of Variable- Coefficient Lanchester-Type Equations of Modern Warfare
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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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 Liouvilles normal form the error which will be incurred by invoking the approximation in a specific situation.
- Military Operations, Strategy and Tactics