Approximation and analysis of confuent hypergeometric differential equation in homing guidance

Abstract

In this paper, we will mainly consider the confluent hypergeometric differential equatin, which models homing guidence system with 1st dynamic lag. In order to reduce the calculation cost of computer loaded at missile, we will find simple approximation of solution of confluent hypergeometric differential equatin. To do this, we need to analyze the closed solution form. Thus using known approxitmation, not good enough but sufficient to explain about behavior of solution, we will derive coefficient of Kummer function. Specially, because of property of Gamma function, when $N=3$, confluent hypergeomtric differential equation has simple form. By expanding solution with Taylor series, we will derive coefficient of series. From these observation, it is reasonable to use perturbation method to obtain simple approximation. By doing this we will form the basis for further research, that explain and control divergence phenomenon.