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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1976
Accession Number
ADA031867

Entities

People

  • James N. Carpenter

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Acquisition
  • Attrition
  • California
  • Computers
  • Differential Equations
  • Errors
  • Integrals
  • Mathematical Analysis
  • Maximum Likelihood Estimation
  • New York
  • Operations Research
  • Parametric Analysis
  • Schools
  • Test And Evaluation
  • United States
  • Warfare
  • Weapon Systems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation
  • Military History / Militaries and War Studies