非线性系统控制方程的齐次扩容精细积分法

基于齐次扩容精细积分法，提出一种新的求解非线性微分方程的高精度预测一校正算法。首先，借助Taylor级数展开，在一个积分步长内将非线性方程转化为线性非齐次方程，然后利用齐次扩容方法，进。一步将其化为线性齐次方程组，便于用精细积分算法求解。为了避免繁琐的导数推导和计算，采用修正Euler法作为预测步、齐次扩容精细积分法进行多次校正计算的方案，获得了较高精度的计算结果。所提出的方法算法简单，编程容易，且避免了系统矩阵的求逆计算，具有更加广泛的应用范围，适用于多自由度、强非线性非保守系统的求解。

Extended Homogeneous Capacity High Precision Integration Method for Control Equation of Nonlinear Systems

Based on extended homogeneous capacity high precision integration method ( EHCHPIM ) , a novel pre-dict-correct method with high accuracy for solving the nonlinear equations is proposed. By means of Taylors formulas and the extended homogeneous capacity method, the nonlinear equation is transferred into a linear homogeneous equation within an integral segment, which can be solved conveniently by the high precision integration method. The scheme of adopting the modified Euler's method as predict-step and the EHCHPIM as correct-step can availably overcome the difficulty of computing higher-order derivatives, and can achieve high accuracy results. Due to no necessity for computing the inverse matrixes of system, the integral interval and calculation efficiency are improved remarkably. The present method admits the application range in nonlinear equations be extended. It is simpler and easier to compile the computer program, and expressly suits for solving the non-conservative systems with multi-DOF and strong nonlinearity.