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Open Access Research Article

Numerical solution algorithm for the model of combat operations under the influence of time delay

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pp. 2011–2023Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2239XML
Received:
08 Oct 2024
Published Online:
28 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2239
Pages:
2011–2023

Abstract

This article presents a mathematical model of the process of delayed combat operations, in which the actions of two sides are delayed by a certain amount of time, based on the interaction of opposing forces, and defines a methodology for numerical solution. Differential equations with delayed arguments allow a more realistic reflection of the dynamic state of processes related to military operations. The article is to propose a finite difference method for numerically solving initial value problems for a system of linear differential equations under the influence of a constant delay time. The algorithm is based on Euler’s method, and a comparative analysis of the proposed method is provided. The combat operations model is considered as a system of functional differential equations with constant delay. The applicability of the proposed approach is demonstrated using examples of conflicts between two opposing sides.

Keywords

Subject Classifications

34K0765Lxx93C23

References

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