中文摘要：

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。

英文摘要：

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.