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本文描述在鱼雷弹道、天线、控制系统等问题中,提出的一类常微分方程的解法——自动积分法。它能自动开始,自动升降积分公式的阶,自动改变积分步长。同时,详细叙述任何多步法[如阿达姆斯(Adams)法]都可通过矩阵变换化为自动积分法。本文也对多步法改变步长和单步截断误差做了新的考虑,提高了解的精确度。因而,它是求解线性或非线性常微分方程的一个有效方法。
This article describes the solution of a class of ordinary differential equations proposed in the torpedo trajectory, antenna, control system and other issues - the automatic integration method. It can automatically start, automatically escalate the order of the integral formula, automatically change the integral step. In the meantime, it is described in detail that any multi-step method [such as Adams method] can be transformed into an automatic integration method by matrix transformation. In this paper, new consideration is also given to the multi-step method to change the step size and single-step truncation error so as to improve the accuracy of understanding. Therefore, it is an effective method to solve linear or nonlinear ordinary differential equations.