基于边界值方法的微分动力系统快速数值计算方法  

Numerical Computation of Differential Dynamic Systems Using Boundary Value Methods

作　　者：陶静静 潘明帅 汪芳宗[1] 

机构地区：[1]三峡大学电气与新能源学院,湖北宜昌443002

出　　处：《三峡大学学报（自然科学版）》2017年第6期71-75,共5页Journal of China Three Gorges University：Natural Sciences

基　　金：国家自然科学基金项目(51377098)

摘　　要：针对非线性微分动力系统的快速求解问题,提出了一种新的数值计算方法,将第二类扩展的隐式梯形积分方法应用于微分动力系统的数值计算.该方法利用扩展的梯形积分方法(ETR2)方法对微分方程进行连续的时间差分离散,然后对离散后的非线性方程组采用牛顿法进行整体求解;利用雅克比矩阵所具有的带状结构特征,采用矩阵方程分裂-组合技巧,避免了对整体雅可比矩阵或多个分块子矩阵进行三角分解,从而提高了数值计算的效率.数值算例结果表明:对于高维非线性微分初值问题的数值计算,本文所提出的数值方法的计算效率与传统隐式梯形法相比具有明显的优势.Aiming at the problem of rapid solution of nonlinear differential dynamical systems, a new numeri- cal method is proposed. The extended trapezoidal rules of the second kind （ETRz） is applied to the computa- tion of differential dynamic system. By using the method, the differential equation used to describe the dy- namic system is discretized continuously within time-domain~ and then the discrete nonlinear difference equa- tion can be solved by the classic Newton method. Taking advantages of the band structure characteristic of Ja- cobi matrix, a special split-combination technique can be used to avoid the matrix faetorization of global ma- trix or multiple block sub-matrices, so as to improve the numerical calculation efficiency. The numerical ex- amples demonstrate that the proposed method is superior to the classic implicit trapezoidal method in compu- tational efficiency.

关 键 词：微分动力系统 初值问题 边界值法 扩展梯形法 

分 类 号：TM744.4[电气工程—电力系统及自动化]