非线性微分动力系统的周期波形松弛响应

Periodic waveform relaxation response of nonlinear differential dynamic systems

目的基于微分动力系统,研究其周期波形松弛响应序列收敛到周期解相对较弱的充分性条件。方法运用微分不等式和范数理论。结果得到了当系统函数满足广义李普希兹条件及弱耗散条件时,波形松弛算法产生的迭代序列收敛到非线性动力系统的周期解的充分性条件,推广了这方面相应的结论。结论所得定理的应用比以前的成果更加广泛。

Aim To obtain some sufficient conditions to safeguard the convergence of waveform relaxation （WR） solutions of a dynamic system described by nonlinear ordinary differential equations with a periodic constraint. Methods Using differential inequality and norm theory. Results A sufficient condition was obtained to safeguard the convergence of waveform relaxation （WR） solutions of a dynamic system described by nonlinear ordinary differential equations with a periodic constrain. Namely, if a basic expression of certain functions issued from the system satisfy certain conditions, the proposed WR algorithm is convergent to the exact solution. Conclusion This sufficient condition is more generalized than previous one.