【摘要】 就一类非线性脉冲比例延迟微分方程(NIPDDEs)，分析了Runge-Kutta方法对于非刚性与刚性情况的收敛性。首先，给出了NIPDDEs的Runge-Kutta方法数值格式。然后，对于非刚性情况，证明了Runge-Kutta方法在求解NIPDDEs时具有经典r阶收敛;对于刚性情况，证明了Runge-Kutta方法在求解NIPDDEs时具有r阶B-收敛。最后，数值试验证实了理论分析的正确性。更多还原

【Abstract】 For a class of nonlinear impulsive pantograph delay differential equations( NIPDDEs),the convergence of Runge-Kutta method for non-stiff and stiff cases was analyzed. Firstly,the Runge-Kutta numerical scheme of NIPDDEs was constructed. Secondly,for the non-stiff case,it was proved that the Runge-Kutta method for solving NIPDDEs is classically convergent with order r,and for the stiff case,it was proved that the Runge-Kutta method for solving NIPDDEs is B-convergent of order r. Finally,numerical experiments confirmed the correctness of the theoretical analysis.更多还原