作　　者： ; ; ; ;

机构地区： 广西科技大学汽车与交通学院

出　　处： 《华中科技大学学报（自然科学版）》 2007年第8期109-111,共3页

摘　　要： 提出了求解非线性动力方程的一种齐次扩容精细积分法.首先利用泰勒公式将动力方程的非线性部分在tk时刻展开至二阶或更高阶级数,然后将1,(t-tk)和(t-tk)2/2等扩充到状态方程中,建立了便于用精细积分法计算的齐次方程形式.该方法能有效避免系统矩阵的求逆问题,且在保证具有较高计算精度的前提下,能使积分步长有效拓宽,提高了计算效率.为适应实际计算,还提出了一种通过迭代修正间接计算导数的方法.计算结果表明所提出的方法具有较好的计算精度和可靠性,是一种求解非线性动力方程的有效方法. An extended homogeneous capacity integration method with high precision to solve nonlinear dynamic equations is proposed. By means of Taylor＇s formulas, the nonlinear part of the dynamic equation is expanded as Taylorrs series with second or higher-order teams at time tk within a integral segment, then extending 1, （t-tk） and （t-tk）2/2 into the state equation, a homogeneous equation which can be solved conveniently by the high precision integration method is established. Due to its unnecessity to compute the inverse matrixes of system, the integral interval and calculation efficiency are improved remarkably. Meanwhile, to adapt for actual calculation, an iterative refinement technique is put forward to overcome the difficulty of computing higher-order derivatives, which not only extends the range of nonlinear dynamic equations, but also is simpler and easier to compile the computer program. Numerical results show that the proposed method is more accurate and reliable.

关 键 词： 非线性动力方程 精细积分法 齐次扩容 迭代修正

领　　域： [理学] [理学] [理学] [理学]