分段连续型延迟Logistic方程Runge-Kutta方法的稳定性  

Stability of Runge-Kutta Methods for Delay Logistic Equations with Piecewise Continuous Arguments

作　　者：胡琳[1,2] 甘四清[2] 张浩敏[2] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075 [2]东北林业大学理学院数学系,哈尔滨150041

出　　处：《系统仿真学报》2009年第22期7033-7036,共4页Journal of System Simulation

基　　金：国家自然科学基金(10871207)

摘　　要：讨论了用Runge-Kutta方法求解分段连续型延迟Logistic方程的稳定性,分析了直接运用Runge-Kutta方法会产生伪解,从而建立了不产生伪解的Runge-Kutta方法,讨论了该方法的收敛阶,证明了该方法是局部和全局渐近稳定的。数值实验进一步验证了算法理论分析的正确性。The stability of Runge-Kutta methods for the delay logistic equations with piecewise continuous arguments was discussed. It is shown that spurious solutions are obtained when Runge-Kutta method is directly applied to the delay logistic equations with piecewise continuous arguments. Runge-Kutta method which does not admit spurious solutions is constructed. The convergence of this method is investigated. It is shown that this method is Olocally asymptotical stable and globally asymptotically stable. Numerical experiment further confirms the theoretical results of numerical analysis.

关 键 词：分段连续 延迟Logistic方程 Runge—Kutta方法 伪解 稳定 

分 类 号：O241.81[理学—计算数学]