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

Abstract

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.