摘要
针对微分动力系统的数值计算,提出二步块边界值方法用于求解线性或非线性微分动力系统。首先,利用二步边界值方法的计算格式离散求解线性或非线性一阶常微分方程,推导得到了通用的计算公式。同时为降低求解方程组的维数,研究采用了二步块边界值方法。在此基础上,通过对两个实际的数值算例进行测试,并将计算结果同精细积分法或微分求积法进行对比。仿真结果表明该方法具有较高的计算精度和良好的数值稳定性,通用性好,可用于求解非线性、强刚性方程。
A two-step block boundary value method is proposed to solve the linear or non-linear differential dynamic system for numerical calculation of differential dynamical systems.Firstly,the linear or non-linear first-order ordinary differential equations are solved by using the computational scheme of two-step boundary value method,and the general formula is deduced.At the same time,in order to reduce the dimension of solving the equations,a twostep block boundary value method is adopted.On the basis of this,two practical numerical examples are tested,and the results are compared with the precise time integration algorithm or the differential quadrature method.The simulation results show that the proposed method has high computational accuracy and good numerical stability,and can be used to solve the non-linear and strong stiff equations.
作者
王阳田
赵孟雨
陈炳文
奕仲飞
曹树立
WANG Yang-tian;ZHAO Meng-yu;CHEN Bing-wen;YI Zhong-fei;CAO Shu-li(College of Electrical Engineering&New Energy,China Three Gorges University,Yichang443002,China)
出处
《电力学报》
2020年第1期1-6,共6页
Journal of Electric Power
关键词
微分动力系统
二步边界值方法
块边界值方法
刚性方程
differential dynamic system
two-step boundary value method
block boundary value method
stiff equation
作者简介
王阳田(1995-),男,硕士研究生,从事配电网自动化及并行运算研究,740360384@qq.com;赵孟雨(1993-),女,硕士研究生,从事配电网自动化及并行运算研究,793652328@qq.com;通信作者:陈炳文(1992-),男,硕士研究生,从事配电网自动化及并行运算研究,1436224855@qq.com;奕仲飞(1994-),男,硕士研究生,从事配电网自动化及并行运算研究,1479270349@qq.com;曹树立(1995-),男,硕士研究生,从事配电网自动化及并行运算研究,237686275@qq.com。
