| 电路模拟中非线性方程的周期波形响应 |
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| 引用本文： | 蔺小林,王晓琴,王玉萍,何广平.电路模拟中非线性方程的周期波形响应[J].哈尔滨工业大学学报,2009,41(3):178-182. |
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| 作者姓名： | 蔺小林 王晓琴 王玉萍 何广平 |
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| 作者单位： | 蔺小林,王晓琴,王玉萍,LIN Xiao-lin,WANG Xiao-qin,WANG Yu-ping(陕西科技大学,理学院,西安,710021);何广平,HE Guang-ping(宝鸡文理学院数学系,宝鸡,721007)
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| 基金项目： | 国家自然科学基会资助项目，陕西科技大学创新基金 |
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| 摘 要： | 用范数估计方法对非线性高阶微分方程的周期边值问题进行了讨论,通过对非线性二阶微分方程周期边值问题的详细讨论,给出了系统函数对某些变量偏导数的某种范数小于1时,非线性二阶微分方程的波形松弛算法产生的迭代序列收敛到该方程的周期解.用类似的方法给出了非线性高阶微分方程的波形松弛算法产生的迭代序列收敛到该方程周期解的充分性条件.
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| 关 键 词： | 非线性高阶微分方程 周期响应 波形松弛 电路模拟 |
Periodic waveform relaxation responses of nonlinear high-order differential equations in circuit simulation |
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| LIN Xiao-lin,WANG Xiao-qin,WANG Yu-ping,HE Guang-ping.Periodic waveform relaxation responses of nonlinear high-order differential equations in circuit simulation[J].Journal of Harbin Institute of Technology,2009,41(3):178-182. |
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| Authors: | LIN Xiao-lin WANG Xiao-qin WANG Yu-ping HE Guang-ping |
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| Affiliation: | 1.Faculty of Science,Shanxi University of Science and Technology,Xi’an 710021,China;2.Mathematics Department,Baoji University of Arts and Science,Baoji 721007,China) |
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| Abstract: | We use norm method to discuss the periodic boundary problems of second and high-order nonlinear differential equations.Present two theorems to safeguard the convergence of waveform relaxation(WR) solutions of a dynamic system described by higher-order implicit nonlinear ordinary differential equations(ODEs) with a periodic constraint.If the norm of functions issued from the system is less than one,the proposed WR algorithm is convergent to the exact solution.And the sufficient conditions to treat periodic solutions of high-order implicit nonlinear ordinary differential equations are provided. |
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| Keywords: | nonlinear high-order differential equations periodic response waveform relaxation circuit simulation |
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