摘要
Treanor显式方法是一种求解刚性常微分方程的数值积分法,用它来解刚性方程时仍然存在一些问题。本文对Treanor方法的稳定性进行了分析和讨论,以Treanor方法为基础,采用Richardson外推技巧,构造出一种改进型方法—T-R预估-校正法。分析和计算都表明,与Treanor方法相比,改进的方法具有更大的稳定域,且提高了数值解的精度。它更适合于刚性方程的求解,是数字仿真中一种较好的数值解法。
Treanor's explicit method is typical among the numerical integrators for ODEs . There is yet some problems when used to cope with stiff equations . In this paper , the stability characteristics of Treanor's method are analyzed and discussed.By using Richardson extrapolation, an improved method based on Treanor's method the Treanor-Richar-dosn predict or-correct or method is suggested . Analysis and numerical computation have made it-clear that the,new method has greater stability region than the Treanor's method and the accuracy of the numerical solution can be increased as compared with that of the Treanor's method . T- R method is more suitable for integration of stiff ODEs . It is a better numerical solver in digital simulations .
出处
《北京理工大学学报》
EI
CAS
CSCD
1990年第1期18-25,共8页
Transactions of Beijing Institute of Technology
关键词
刚性常微分方程
T-R预估
数值解
常微分方程
digital simulation, stiff ordinary differential equations stability , stiff stability, hydraulic system .
