一类时滞兰彻斯特方程的奇异摄动方法

摘要

Considering the important role of Lanchester equation of reaction time factor in combat elements, time delay Lanchester combat model is established under the condition of informationization. Each approximate solution of Lanchester equation using singular perturbation theory was constructed by constructing boundary layer function method, then comparing the accuracies for the solutions verifies the asymptotic expansion possesses a better accuracy and this kind of approximate solution is analyzing, thus further qualitative and quantitative research on the Lanchester equation can be done on this basic research.%考虑兰彻斯特方程反应时间因素在战斗要素中的重要作用，建立信息化条件下的时滞兰彻斯特战斗模型。通过构造边界层函数，用时滞奇异摄动理论研究时滞兰彻斯特方程的各次近似解，并对解进行精度比较。结果表明：该奇异摄动方法简单、有效，具有较高的精度，能得到解的表达式以及解析运算，可进一步对兰彻斯特方程进行定性及定量的研究。