非线性脉冲微分方程Runge-Kutta方法的渐近稳定性（英文）  

Asymptotic stability of explicit Runge-Kutta methods for nonlinear impulsive differential equations

作　　者：张贵来 张玲 ZHANG Guilai;ZHANG Ling(School of Mathematics and Statistics,Northeastern University at Qinhuangdao,Qinhuangdao 066004,China;Teacher Education Institute,Daqing Normal University,Daqing 163712,China)

机构地区：[1]东北大学秦皇岛分校数学与统计学院,秦皇岛066004 [2]大庆师范学院教师教育学院,大庆163712

出　　处：《黑龙江大学自然科学学报》2018年第4期424-432,共9页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundations of Hebei Province(A2015501130);the Research Project of Higher School Science and Technology in Hebei Province(ZD2015211);the Fundamental Research Funds for Central Universities(N152304007);the Youth Science Foundations of Heilongjiang Province(QC2016001)

摘　　要：研究非线性脉冲微分方程在全局Lipschitz条件下,精确解和Runge-Kutta方法数值解的渐近稳定性;在非线性函数满足Lipschitz条件下,给出解析解渐近稳定的条件;讨论几类显式RungeKutta方法应用于该方程时数值解渐近稳定的条件,证明在满足收敛阶的条件下,数值解可以保持解析解的渐近稳定性,当p≤4时,上述结论成立,当p> 4时,上述结论不成立。数值算例验证了结果的有效性。Asymptotic stability of both the exact and numerical solutions to nonlinear impulsive differential equations is dealt with. Asymptotic stability of the exact solution of impulsive differential equations is studied under the Lipschitz conditions. It is proved that the p -stage pth order explicit Runge-Kutta methods whose coefficients are nonnegative preserve asymptotic stability of the exact solutions of impulsive differential equations under the Lipschitz conditions, when p ≤ 4. A numerical experiment is given to illustrate the conclusions.

关 键 词：脉冲微分方程 显式Runge—Kutta方法 LIPSCHITZ条件 渐近稳定 

分 类 号：O189.1[理学—数学]