MA Yan， ZHAO Han-dong， XU Jin-peng， ZHU Fu-lin
(School of Mechatronic Engineering, North University of China, Taiyuan 030051, China)
Abstract： Several numerical methods of differential equations and their applications in ballistic calculation are discussed for the purpose of simplification of the dynamic differential equations of projectile trajectory. Program simulations of Euler method, Heun method, lassic fourth-order Runge Kutta (RK4) method, ABM method and Hamming method are achieved based on Matlab. In addtion, the approximate solutions, local truncation errors and calculation time of the dynamic differential equations are obtained. By analyzing the simultaion results, the advantages and disadvantages of these methods are compared, which provides a basis for choice of ballistic calculation methods.
Key words： classic fourth-order Runge Kutta (RK4) method； ballistic calculation； calculation time
CLD number： TP391 Document code： A
Article ID： 1674-8042（2016）01-0035-05 doi： 10.3969/j.issn.1674-8042.2016.01.007
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几种数值算法在弹道微分方程组解算中的仿真与比较
马 焱， 赵捍东， 许金鹏， 朱福林
（中北大学 机电工程学院， 山西 太原 030051）
摘 要： 本文简述了数值分析的应用范围， 介绍了微分方程几种不同的数值解法， 及其在弹道解算中的应用。 在简化弹丸弹道动力学微分方程的基础上， 通过Mablab软件编写欧拉法、 梯形法、 经典四阶龙格库塔法程序， 计算动力学微分方程组近似解及各种方法的局部截断误差和计算时间。 通过对结果的分析比较， 明确了几种经典解法在弹道解算中的优劣， 为弹道解算方法的选择提供了依据。
关键词： 经典四阶龙格库塔法； 弹道解算； 解算时间
引用格式： MA Yan， ZHAO Han-dong， XU Jin-peng， et al. Simulation and comparison of several numerical algorithms for solving ballistic differential equations. Journal of Measurement Science and Instrumentation, 2016, 7(1)： 35-39. ［doi： 10. 3969／j. issn. 1674-8042.2016.01.007］
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