自治常微分方程欧拉法的长时间收敛性和误差估计  

Long-time convergence and error estimates of Euler methods to autonomous ordinary differential equation

作　　者：张法勇[1] ZHANG Fayong(School of Mathematical Sciences,Heilongjiang University,Harbin 100080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2020年第6期631-637,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(10371077)。

摘　　要：利用向前和向后欧拉法研究了自治常微分方程趋于其渐进稳定的双曲平衡点的解的逼近,得到了向前和向后欧拉法的解在无界时间区间[0,∞)上的最优误差估计。几个数值试验验证了理论分析的正确性。The approximation of solutions of autonomous ordinary differential equation that approach asymptotically stable hyperbolic equilibrium point is considered by the forward and backward Euler methods. The optimal error estimates that hold uniformly on unbounded time interval [0, ∞) are obtained for the forward and backward Euler methods. Several numerical experiments are carried out to verify the theoretical analysis.

关 键 词：自治常微分方程 欧拉法 长时间收敛性和误差估计 

分 类 号：O241.81[理学—计算数学]