Battle-outcome prediction for an extended system of Lanchester-type differential equations
type: Item
instance of: scholarly article
title: Battle-outcome prediction for an extended system of Lanchester-type differential equations
zbMATH Open document ID: 0588.34037
DOI: 10.1016/0022-247X(84)90134-3
author: James G. Taylor
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Battle-outcome-prediction conditions are given for an extended system of Lanchester-type differential equations for two different types of battle- termination conditions: (a) fixed-force-level-breakpoint battles, and (b) fixed-force-ratio-breakpoint battles. Necessary and sufficient conditions for predicting battle outcome are given in the former case for a fight to the finish, while sufficient conditions are given in the latter case. The former results are equivalent to those for the problem of classical analysis of determining (explicitly as a function of the initial conditions) the occurrence of a zero point for the solution to this extended system, although such results as given here have not appeared previously for nonoscillatory (in the strict sense) solutions.
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 3944333
zbMATH Keywords: first order differential equation
zbMATH Keywords: Lanchester-type differential equations
zbMATH Keywords: battle-termination conditions
MaRDI profile type: Publication
cites work: Present State of the Lanchester Theory of Combat
cites work: Q5570370
cites work: Properties of Solutions of $u'' + c(t)f(u)h(u') = 0$ with Explicit Initial Conditions
cites work: Terminal Value Problems for Second Order Nonlinear Differential Equations
cites work: Error Bounds for the Liouville-Green Approximation to Initial-Value Problems
cites work: Prediction of Zero Points of Solutions to Lanchester-Type Differential Combat Equations for Modern Warfare
cites work: Battle-outcome-prediction conditions for variable-coefficient Lanchester- type equations for area fire
cites work: Improved error bounds for the Liouville Green (or WKB) approximation
cites work: Analysis of the functional dependence of the modified parity-condition parameter on its argument for an important class of Lanchester-type equations for modern warfare†
cites work: Force-Ratio Considerations for Some Lanchester-Type Models of Warfare
description: scientific article; zbMATH DE number 3944333